solving inequality word problems worksheet

Inequalities Word Problems Worksheets

Inequalities word problems worksheets can help encourage students to read and think about the questions, rather than simply recognizing a pattern to the solutions.Inequalities word problems worksheet come with the answer key and detailed solutions which the students can refer to anytime.

Benefits of Inequalities Word Problems Worksheets

Inequalities word problems worksheets help kids to improve their speed, accuracy, logical and reasoning skills.

Inequalities word problems worksheets gives students the opportunity to solve a wide variety of problems helping them to build a robust mathematical foundation. Inequalities word problems worksheets helps kids to improve their speed, accuracy, logical and reasoning skills in performing simple calculations related to the topic of inequalities.

Inequalities word problems worksheets are also helpful for students to prepare for various competitive exams.

These worksheets come with visual simulation for students to see the problems in action, and provides a detailed step-by-step solution for students to understand the process better, and a worksheet properly explained about the Inequalities.

Download Inequalities Word Problems Worksheet PDFs

These math worksheets should be practiced regularly and are free to download in PDF formats.

☛ Check Grade wise Inequalities Word Problems Worksheets

• 7th Grade Inequalities Worksheets

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Writing Inequalities from Word Problems

Learn about writing inequalities from word problems with help from our practice examples. If you want to test yourself, or get some practice, then try one of our graded worksheets, or our online quiz.

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What is an Inequality?

The language of inequalities.

• How to Write an Inequality from a Word Problem
• Write an Inequality from a Word Problems Examples

Writing Inequalities from Word Problems Worksheets

• Writing Inequalities from Word Problems Online Quiz
• More related resources

An inequality is when you have a relationship between two values of expressions which are not equal to each other.

There are a few different options for different types of inequalities:

• Greater than (>) where one expression or value is greater than another, e.g. 7 > 5
• Less than (<) where one expression or value is less than another, e.g. 9 < 2 x 6
• Greater than or equal to (≥) where one expression or value is greater than or equal to another, e.g. 20 + 4 ≥ 17
• Less than or equal to (≤) where one expression or value is less than or equal to another, e.g. 18 ≤ 9 x 2
• Not equal to (≠) where one expression or value is not equal to another, e.g. 7 ≠ 4

When writing inequalities from word problems, we have to look carefully at and understand the language being used.

Different words and phrases have different meanings when deciding on which inequality to use.

The mathematical notation is really just a shorthand way of writing the words more efficiently and clearly.

Here is a quick table showing some of the written expressions often used and which inequality they are represented by.

Note: the word 'between' is mainly used to mean between inclusively (including end points).

However, sometimes 'between' is used to mean between exclusively (excluding end points).

To avoid ambiguity, it is good practice to include the word 'inclusive' or 'exclusive' to make it completely clear if the end points are included or not.

Some simple examples showing inequalities from phrases:

The variable names (letters) have been chosen at random - you can use any variable name to represent any value.

Note: you need to read the word problem carefully because sometimes the inequality does not match the language used, especially when the inequality involves finding out what is left over or what remains after an amount is taken away. See Examples 2) and 7) below.

How to Write Inequalities from Word Problems

When we are writing an inequality from a word problem, we are basically translating the word problem into mathematical language and symbols.

When writing an inequality from a word problem, there are two simple steps you need to follow...

Step 1) Read the word problem carefully and change the word problem into algebra.

• use the language of inequalities table to help you select the right inequality

Step 2) Use algebra to solve the word problem

Step 3) rewrite the inequality using algebra., write an inequality from a word problem examples.

The best way to learn how to write inequalities from word problems and see how they work is to look at some ready made examples.

Writing Inequalities from Word Problems - Basic Examples

Here are some examples of writing inequalities from word problems.

Example 1) Sally bakes some cookies and needs to put them in the over for at least 12 minutes. Write an inequality using the variable t to show how long the cookies need to be baked in the oven.

The vocabulary which tells us about the inequality are the words: at least .

This means we need to use the ≥ symbol.

So the inequality is t ≥ 12 minutes

Example 2) Newton has a 30 ounce bottle of water. He drinks over half of the bottle. Write an inequality using the variable c to show how many ounces are left in the bottle.

The vocabulary which tells us about the inequality are the words: over .

However, because he has drunk over half the bottle, it means that there is under half a bottle left.

So the symbol we need is < and the amount is ½ of 30 = 15.

So the inequality is b < 15 ounces

Example 3) Anna is more than three times as old as Bertie. If Bertie is 8 years old, write an inequality using the variable A to show how old Anna is.

The vocabulary which tells us about the inequality are the words: more than .

So the symbol we need is > and the amount is 3 x 8 = 24.

So the inequality is A > 24 years old

Example 4) A book has 14 chapters.The shortest chapter has 12 pages. Write an inequality using the variable p to show how many pages the book has.

The vocabulary which tells us about the inequality are the words: shortest .

If the shortest chapter has 11 pages, then there must be some chapters with more than 11 pages.

So the symbol we need is > and the amount is 14 x 12 = 168.

So the inequality is p > 168 pages.

Writing Inequalities from Word Problems -Intermediate Examples

These examples use two different variables and express one variable in terms of another.

Example 5) Captain and Frazer have some gold coins. Captain has at least three times as many coins as Frazer. Write an inequality for the number of coins Captain has (c) in terms of the number of coins Frazer has (f).

So the symbol we need is ≥

So the inequality is c ≥ 3f.

Example 6) In a hotel there are f flights of stairs. Each flight has a maximum of 12 steps. There are also 3 steps up to the main entrance. Write an expression for the total number of steps, s, in terms of f.

The vocabulary which tells us about the inequality are the words: a maximum of .

So the symbol we need is ≤

We know that there are f flights of steps and also 3 extra steps.

So the inequality is s ≤ 12f + 3.

Writing Inequalities from Word Problems - Harder Examples

These examples involve solving word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers.

There are also examples where the variable lies between two values.

Example 7) Captain has a one-liter bottle of water. He drinks more than one-quarter of the bottle but less than one-half of the bottle. Write an inequality using the variable b to show the amount of water than is left in the bottle.

The vocabulary which tells us about the inequality are the words: more than and less than .

However, because we are looking at what is left in the bottle, rather than what has been drunk, we need to think carefully about the inequalities!

He drinks more than one-quarter of the bottle, so there will be less than three-quarters of the bottle left, so we need the symbol <

He drinks less than one-half of the bottle, so there will be one-half or more of the bottle left, so we need the symbol ≥

Half of the bottle = ½ liters = 500 ml. 1000 - 500 = 500 ml

Quarter of the bottle = ¼ liters = 250 ml. 1000 - 250 = 750 ml

So the inequality is b ≥ 500 ml and b < 750 ml This can be simplified to: 500 ≤ b < 750 ml This means that he has at least 500 ml but less than 750 ml left.

Example 8) Captain has challenged himself to catch a minimum of 50 fish from a lake. He manages to catch 8 of them and put them in his bucket. If he catches 6 fish every hour, write an inequality to show the time (t) in hours it will take him to reach his target.

The vocabulary which tells us about the inequality are the words: a minimum of .

The inequality we get from this problem is 6t + 8 ≥ 50

We are not finished yet, because this needs to be simplified and written in terms of t.

6t + 8 ≥ 50 so 6t ≥ 42

If we divide both sides of this inequality by 6, we get:

So the inequality is t ≥ 7 hours He needs to fish for at least 7 hours to reach his target.

Example 9) It takes Newton between 23 and 28 seconds (inclusive) to swim a length of a swimming pool. Write an inequality using the variable t to show how long it will take him to swim 3 lengths.

The vocabulary which tells us about the inequality are the words: between (inclusive) .

So the symbol we need is ≤ and ≥

3 x 23 = 69 and 3 x 28 = 84

So the inequality is t ≥ 69 and t ≤ 84 This can be simplified to: 69 ≤ t ≤ 84 It will take him between 69 and 84 seconds (inclusive) to swim 3 lengths.

We have a range of different inequality worksheets which involve writing inequalities from a range of word problems..

We have split the sheets into 3 sections: A, B and C

• Section A involves basic level questions aimed at 6th grade
• Section B involves medium level questions aimed at 6th and 7th grade
• Section C involves more advanced questions aimed at 7th and 8th grade

Writing Inequalities from Word Problems - Section A Easier

Sheet 1 involves picking the vocabulary and relevant information from the problem and writing the inequality

Sheet 2 involves the same skills as Sheet 1, but also involves an arithmetic operation to get the inequality.

• Inequalities from Word Problems Sheet A1
• PDF version
• Inequalities from Word Problems Sheet A2

Writing Inequalities from Word Problems - Section B Medium

Sheet 1 involves using two variables and writing an inequality for one variable in terms of the other variable

Sheet 2 is similar to Sheet 1 but with slightly harder problems.

• Inequalities from Word Problems Sheet B1
• Inequalities from Word Problems Sheet B2

Writing Inequalities from Word Problems - Section C

Sheet 1 involves using one variables and using the information to solve the inequality, usually in the form px + q > r or px + q < r, where p, q, and r are specific rational numbers

Sheet 2 involves the same skills as Sheet 1 but has compound inequalities in each question

• Inequalities from Word Problems Sheet C1
• Inequalities from Word Problems Sheet C2

More Recommended Math Worksheets

Take a look at some more of our worksheets similar to these.

Inequalities on a Number Line Worksheets

• Inequalities on a Number Line

6th Grade Ratio and Unit Rate Worksheets

These 5th grade ratio worksheets are a great way to introduce this concept.

We have a range of part to part ratio worksheets and slightly harder problem solving worksheets.

• Ratio Part to Part Worksheets
• Ratio and Proportion Worksheets
• The Definition of Unit Rate
• Unit Rate Problems 6th Grade

6th Grade Algebra Worksheets

If you are looking for some 6th grade algebra worksheets to use with your child to help them understand simple equations then try our selection of basic algebra worksheets.

There are a range of 6th grade math worksheets covering the following concepts:

• Generate the algebra - and write your own algebraic expressions;
• Calculate the algebra - work out the value of different expressions;
• Solve the algebra - find the value of the term in the equation.
• Use the distributive property to factorize and expand different expressions
• 6th Grade Distributive Property Worksheets
• Expressions and Equations 6th Grade
• Basic Algebra Worksheets (6th & 7th Grade)

Writing Inequalities from Word Problems Quiz

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This quick quiz tests your skill at writing inequalities from a range of word problems.

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Free Linear Inequalities Word Problems Worksheet

While teaching high school, one of the biggest struggles I have seen students face is applying math concepts to the real-world. This is true when it comes to solving linear inequalities word problems too. Students often find it challenging to grasp how these mathematical principles translate into practical, everyday life scenarios.

That’s why I have put together this linear inequalities word problems worksheet! My goal is to help you learn a few tips and tricks and practice applying linear inequalities to the real-world! 

What are Linear Inequality Word Problems?

Lesson plans that focus on linear inequality word problems typically show students how to apply the skills they developed while solving inequalities to the real-world. There are a wide variety of inequality applications, ranging from social studies to physical science. Regardless of the application, the idea is that you will be faced with a word problem that requires you to model the scenario using a linear inequality.

In general, linear inequality word problems describe how one quantity has to be less than or greater than another. Your goal is then to use inequality symbols and  algebraic expressions  to represent the scenario algebraically.

For most, the concept of a linear inequality is first introduced in middle school (although this will vary by curriculum). My daughter, for example, is in 2nd grade math and is just starting to explore these problems. Others may not see this concept until later in high school (in some cases not until the 12th grade).

How to Solve a Linear Inequality Word Problem

The best way to solve any math word problem is to start by reading the question very carefully, and linear inequality word problems are no different!

I always encourage my students to underline or highlight any key words and important information. When it comes to how to solve a linear inequality word problem, the key words usually help you understand:

• which quantities you are working with
• whether you are working with  less than  or  greater than symbols

Once you have identified this important information, your goal is to write an algebraic expression using an inequality symbol that models the scenario. You can then solve the inequality using a similar process to what you would apply when solving one-step equations or  two step equations .

There are many different ways to represent the solution to an inequality problem. Sometimes you will be asked to use a number line, which shows all the negative values or positive values that belong to a solution set. The worksheet attached below will provide you with some practice using number lines to communicate your answers to inequality word problems.

​Solving a Linear Inequality Word Problem Example

Age problems are common applications that you will see when solving linear inequality word problems. These types of problems can be simple or complex, but I wanted to start by sharing a simple one here so that you can understand the basics of how to solve linear inequality word problems.

A father is 3 times as old as his son, but three times his son’s age is less than 30. What is the oldest the son can be?

We can begin by calling out the key words that give us important information. In this case, the following two pieces of information are considered important to the problem:

• “3 times as old as”
• “less than 30”

This tells us that we will be working with a “<” symbol, and multiplication of a quantity by 3. If we let  n  represent the age of the son, we can set up a linear inequality as follows:

$$3n<30$$

Reading this statement in English tells us that “3 times the son’s age is less than 30”. If you head back to the original problem, that seems to match the scenario given, doesn’t it? Great! That tells us that we have a good algebraic model for our real-world problem! Let’s move on and start solving!

Remember that we can solve a linear inequality using algebra in a similar way to solving a linear equation. This means that we can add or subtract terms on both sides of the inequality symbol, and we can also multiply and divide terms on both sides of the inequality symbol.

In this case, since we are multiplying  n  by 3, we divide both sides by 3 to isolate  n.

$$\frac{3n}{3}< \frac{30}{3}$$

$$n<10$$

This tells us that the son’s age must be less than 10 in order for the father to be three times his age but still less than 30 years old himself.

We can test this by multiplying a number greater than 10 by 3. For example, \(11 \times 3 = 33\). Notice that 33 is  not  less than 30. Therefore the son cannot be 11. The only values that will make this inequality statement true are values that are less than (not including) 10.

We can represent this solution on a number line by placing a hollow circle at 10 and drawing an arrow to the left toward the negative values. However, we should stop at zero since the son’s age cannot be less than zero. Note that the son must also not be equal to zero. If he were, the father would be \(3 \times 0 = 0\) as well!

If you need more practice with the algebra strategies that can be used to solve inequalities, check out this collection of  solving linear inequalities worksheets .

Linear Inequalities Word Problems Worksheet

Now that you have had some practice applying your understanding of linear inequalities to solve a real-world problem, you are ready to practice! Below I have included a linear inequalities word problem worksheet that covers a variety of problem types, ranging from age problems, to a bake sale problem with pink cupcakes!

As promised, this worksheet will also provide you with practice representing the solution to a linear inequality word problem on a number line. While you should be sure to attempt every problem as independent work first, make sure that you also check the answer key! This is an important step to make sure that you fully understand each problem.

My hope is that you find this linear inequalities word problems worksheet helpful as independent work whether you are in 1st grade math, 7th grade math, or anything in between!

Download the PDF worksheet by clicking below!

Practice Solving Linear Inequalities Word Problems

I hope this linear inequalities word problems worksheet has provided you with some practice with applying this important math concept to the real-world! My goal was to share examples that cover a variety of areas of life. Hopefully solving these problems also gave you an appreciation for how linear inequalities can be used in everyday life.

Whether you first learned about linear inequality word problems in the 6th grade or are just experiencing them for the first time in the 12th grade, the most important thing you can do is practice. Solving many different types of linear inequalities word problems will help you start to recognize patterns. This will help you with the first initial step of writing the inequality as an algebraic statement, something many students find challenging! 

With consistent practice, you’ll develop a strong foundation in solving linear inequalities, enhancing your problem-solving skills and confidence in applying mathematical concepts to diverse real-world scenarios. Keep exploring and practicing, and you’ll find that handling linear inequalities becomes more intuitive over time!

If you are looking for more word problem resources, check out this linear equations word problems worksheet !

Did you find this linear inequalities word problems worksheet helpful? Share this post and subscribe to Math By The Pixel on YouTube for more helpful mathematics content!

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Last modified on April 17th, 2024

Inequality Word Problems

Inequalities are common in our everyday life. They help us express relationships between quantities that are unequal. Writing and solving word problems involving them helps develop our problem-solving approach, understanding, logical reasoning, and analytical skills.

Here are the 4 main keywords commonly used to write mathematical expressions involving inequalities.   

• At least →  ‘greater than or equal to’
• More than → ‘greater than’
• No more than or at most → ‘less than or equal to’
• Less than → ‘less than’

To participate in the annual sports day, Mr. Adams would like to have nine students in each group. But fewer than 54 students are in class today, so Mr. Adams is unable to make as many full groups as he wants. How many full groups can Mr. Adams make? Write the inequality that describes the situation.

Let ‘x’ be the total number of groups Mr. Adams can make. Since each group has 9 students, the total number of students in ‘x’ groups is 9x As we know, fewer than 54 students are in a class today. Thus, the inequality that represents the situation is: 9x < 54 On dividing both sides by 9, the maximum number of groups Mr. Adams can make is  x < 6 Thus, Mr. Adams can make a maximum of 6 full groups.

 Bruce needs at least \$561 to buy a new tablet. He has already saved \$121 and earns \$44 per month as a part-timer in a company. Write the inequality and determine how long he has to work to buy the tablet.

Let ‘x’ be the number of months Bruce needs to work. As we know,  The amount already saved by Bruce is \$121 He earns \$44 per month The cost of the tablet is at least \$561 After ‘x’ months of work, Bruce will have \$(121 + 44x) Now, the inequality representing the situation is: 121 + 44x ≥ 561 On subtracting 121 from both sides, 121 + 44x – 121 ≥ 561 – 121 ⇒ 44x ≥ 440 On dividing both sides by 44, x ≥ 10 Thus, Bruce needs to work for at least 10 months to buy the new tablet.

A store is offering a \$26 discount on all women’s clothes. Ava is looking at clothes originally priced between \$199 and \$299. How much can she expect to spend after the discount?

Let ‘x’ be the original price of the clothes Ava chooses. As we know, the original price range is 199 ≤ x ≤ 299, and the discount is \$26 Now, Ava pays \$(x – 26) after the discount. Thus, the inequality is: 199 – 26 ≤ x – 26 ≤ 299 – 26 ⇒ 173 ≤ x – 26 ≤ 273 Thus, she can expect to spend between \$173 and \$273 after the discount.

A florist makes a profit of \$6.25 per plant. If the store wants to profit at least \$4225, how many plants does it need to sell?

Let ‘P’ be the profit, ‘p’ be the profit per plant, and ‘n’ be the number of plants.  As we know, the store wants a profit of at least \$4225, and the florist makes a profit of \$6.25 per plant. Here, P ≥ 4225 and p = 6.25 …..(i) Also, P = p × n Substituting the values of (i), we get 6.25 × n ≥ 4225 On dividing both sides by 6.25, we get ${n\geq \dfrac{4225}{6\cdot 25}}$ ⇒ ${n\geq 676}$ Thus, the store needs to sell at least 676 plants to make a profit of \$4225.

Daniel had \$1200 in his savings account at the start of the year, but he withdraws \$60 each month to spend on transportation. He wants to have at least \$300 in the account at the end of the year. How many months can Daniel withdraw money from the account?

As we know, Daniel had \$1200 in his savings account at the start of the year, but he withdrew \$60 for transportation each month.  Thus, after ‘n’ months, he will have \$(1200−60n) left in his account. Also, Daniel wants to have at least \$300 in the account at the end of the year.  Here, the inequality is: 1200 – 60n ≥ 300 ⇒ 1200 – 60n – 1200 ≥ 300 – 1200 (by subtraction property) ⇒ -60n ≥ -900 ⇒ 60n ≤ 900 (by inversion property) ⇒ n ≤ ${\dfrac{900}{60}}$ ⇒ n ≤ 15 Thus, Daniel can withdraw money from the account for at most 15 months.

Anne is a model trying to lose weight for an upcoming beauty pageant. She currently weighs 165 lb. If she cuts 2 lb per week, how long will it take her to weigh less than 155 lb?

Let ‘t’ be the number of weeks to weigh less than 155 lb. As we know, Anne initially weighs 165 lb After ‘t’ weeks of cutting 2 lb per week, her weight will be 165 – 2t Now, Anne’s weight will be less than 155 lb Here, the inequality from the given word problem is: 165 – 2t < 155 On subtracting 165 from both sides, we get 165 – 2t – 165 < 155 – 165 ⇒ – 2t < -10 On dividing by -2, the inequality sign is reversed. ${\dfrac{-2t}{-2} >\dfrac{-10}{-2}}$ ⇒ t > 5

Rory and Cinder are on the same debate team. In one topic, Rory scored 5 points more than Cinder, but they scored less than 19 together. What are the possible points Rory scored?

Let Rory’s score be ‘r,’ and Cinder’s score be ‘c.’ As we know, Rory scored 5 points more than Cinder. Thus, Rory’s score is r = c + 5 …..(i) Also, their scores sum up to less than 19 points. Thus, the inequality is: r + c < 19 …..(ii) Substituting (i) in (ii), we get (c + 5) + c < 19 ⇒ 2c + 5 < 19 On subtracting 5 from both sides, we get 2c + 5 – 5 < 19 – 5 ⇒ 2c < 14 On dividing both sides by 2, we get ${\dfrac{2c}{2} >\dfrac{14}{2}}$ ⇒ c < 7 means Cinder’s score is less than 7 points. Now, from (i), r = c + 5 ⇒ c = r – 5 Thus, c < 7 ⇒ r – 5 < 7 On adding 5 to both sides, we get r – 5 + 5 < 7 + 5 ⇒ r < 12 means Rory’s score is less than 12 points. Hence, Rory’s scores can be 6, 7, 8, 9, 10, or 11 points.

An average carton of juice cans contains 74 pieces, but the number can vary by 4. Find out the maximum and minimum number of cans that can be present in a carton.

Let ‘c’ be the number of juice cans in a carton. As we know, the average number of cans in a carton is 74, and it varies by 4 cans. Thus, the required inequality is |c – 74| ≤ 4 ⇒ -4 ≤ c – 74 ≤ 4 On adding 74 to each side, we get -4 + 74 ≤ c – 74 + 74 ≤ 4 + 74 ⇒ 70 ≤ c ≤ 78 Hence, the minimum number of cans in a carton is 70, and the maximum number is 78.

 Layla rehearses singing for at least 12 hours per week, for three-fourths of an hour each session. If she has already sung 3 hours this week, how many more sessions remain for her to exceed her weekly practice goal?

Let ‘p’ be Layla’s total hours of practice in a week, and ‘s’ be the number of sessions she needs to complete. As we know, Layla has already rehearsed 3 hours, then her remaining rehearsal time is (p – 3) Each session lasts for three-fourths of an hour. Thus, we have the inequality: ${\dfrac{3}{4}s >p-3}$ …..(i) As we know, Layla rehearses for at least 12 hours, which means p ≥ 12 …..(ii) From (i), ${\dfrac{3}{4}s >p-3}$ ⇒ ${s >\dfrac{4}{3}\left( p-3\right)}$ From (ii), substituting the value p = 12 in (i), we get ${s >\dfrac{4}{3}\left( 12-3\right)}$ ⇒ ${s >\dfrac{4}{3}\cdot 9}$ ⇒ s > 12 Thus, Layla must complete more than 12 sessions to exceed her weekly rehearsal goal.

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Solving Inequality Word Questions

(You might like to read Introduction to Inequalities and Solving Inequalities first.)

In Algebra we have "inequality" questions like:

Sam and Alex play in the same soccer team. Last Saturday Alex scored 3 more goals than Sam, but together they scored less than 9 goals. What are the possible number of goals Alex scored?

How do we solve them?

The trick is to break the solution into two parts:

Turn the English into Algebra.

Then use Algebra to solve.

Turning English into Algebra

To turn the English into Algebra it helps to:

• Read the whole thing first
• Do a sketch if needed
• Assign letters for the values
• Find or work out formulas

We should also write down what is actually being asked for , so we know where we are going and when we have arrived!

The best way to learn this is by example, so let's try our first example:

Assign Letters:

• the number of goals Alex scored: A
• the number of goals Sam scored: S

We know that Alex scored 3 more goals than Sam did, so: A = S + 3

And we know that together they scored less than 9 goals: S + A < 9

We are being asked for how many goals Alex might have scored: A

Sam scored less than 3 goals, which means that Sam could have scored 0, 1 or 2 goals.

Alex scored 3 more goals than Sam did, so Alex could have scored 3, 4, or 5 goals .

• When S = 0, then A = 3 and S + A = 3, and 3 < 9 is correct
• When S = 1, then A = 4 and S + A = 5, and 5 < 9 is correct
• When S = 2, then A = 5 and S + A = 7, and 7 < 9 is correct
• (But when S = 3, then A = 6 and S + A = 9, and 9 < 9 is incorrect)

Lots More Examples!

Example: Of 8 pups, there are more girls than boys. How many girl pups could there be?

• the number of girls: g
• the number of boys: b

We know that there are 8 pups, so: g + b = 8, which can be rearranged to

We also know there are more girls than boys, so:

We are being asked for the number of girl pups: g

So there could be 5, 6, 7 or 8 girl pups.

Could there be 8 girl pups? Then there would be no boys at all, and the question isn't clear on that point (sometimes questions are like that).

• When g = 8, then b = 0 and g > b is correct (but is b = 0 allowed?)
• When g = 7, then b = 1 and g > b is correct
• When g = 6, then b = 2 and g > b is correct
• When g = 5, then b = 3 and g > b is correct
• (But if g = 4, then b = 4 and g > b is incorrect)

A speedy example:

Example: Joe enters a race where he has to cycle and run. He cycles a distance of 25 km, and then runs for 20 km. His average running speed is half of his average cycling speed. Joe completes the race in less than 2½ hours, what can we say about his average speeds?

• Average running speed: s
• So average cycling speed: 2s
• Speed = Distance Time
• Which can be rearranged to: Time = Distance Speed

We are being asked for his average speeds: s and 2s

The race is divided into two parts:

• Distance = 25 km
• Average speed = 2s km/h
• So Time = Distance Average Speed = 25 2s hours
• Distance = 20 km
• Average speed = s km/h
• So Time = Distance Average Speed = 20 s hours

Joe completes the race in less than 2½ hours

• The total time < 2½
• 25 2s + 20 s < 2½

So his average speed running is greater than 13 km/h and his average speed cycling is greater than 26 km/h

In this example we get to use two inequalities at once:

Example: The velocity v m/s of a ball thrown directly up in the air is given by v = 20 − 10t , where t is the time in seconds. At what times will the velocity be between 10 m/s and 15 m/s?

• velocity in m/s: v
• the time in seconds: t
• v = 20 − 10t

We are being asked for the time t when v is between 5 and 15 m/s:

So the velocity is between 10 m/s and 15 m/s between 0.5 and 1 second after.

And a reasonably hard example to finish with:

Example: A rectangular room fits at least 7 tables that each have 1 square meter of surface area. The perimeter of the room is 16 m. What could the width and length of the room be?

Make a sketch: we don't know the size of the tables, only their area, they may fit perfectly or not!

• the length of the room: L
• the width of the room: W

The formula for the perimeter is 2(W + L) , and we know it is 16 m

• 2(W + L) = 16
• L = 8 − W

We also know the area of a rectangle is the width times the length: Area = W × L

And the area must be greater than or equal to 7:

• W × L ≥ 7

We are being asked for the possible values of W and L

Let's solve:

So the width must be between 1 m and 7 m (inclusive) and the length is 8−width .

• Say W = 1, then L = 8−1 = 7, and A = 1 x 7 = 7 m 2 (fits exactly 7 tables)
• Say W = 0.9 (less than 1), then L = 7.1, and A = 0.9 x 7.1 = 6.39 m 2 (7 won't fit)
• Say W = 1.1 (just above 1), then L = 6.9, and A = 1.1 x 6.9 = 7.59 m 2 (7 fit easily)
• Likewise for W around 7 m

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Note: this page contains legacy resources that are no longer supported. You are free to continue using these materials but we can only support our current worksheets , available as part of our membership offering .

Inequalities Word Problems Worksheet

Related resources.

The various resources listed below are aligned to the same standard, (7EE04) taken from the CCSM ( Common Core Standards For Mathematics) as the Expressions and equations Worksheet shown above.

Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.

• Solve word problems leading to equations of the form  px  +  q  =  r  and  p ( x  +  q ) =  r , where  p ,  q , and  r  are specific rational numbers . Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach.  For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?
• Solve word problems leading to inequalities of the form  px  +  q  >  r  or  px  +  q  <  r , where  p ,  q , and  r  are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem.  For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.

Example/Guidance

• Solving Simple Equations in 2 Steps

Similar to the above listing, the resources below are aligned to related standards in the Common Core For Mathematics that together support the following learning outcome:

Solve real-life and mathematical problems using numerical and algebraic expressions and equations

• Equations with subtraction  e.g. x – 4 = 2 (From Worksheet)
• Equations with division  e.g. n/2 = 12 (From Worksheet)
• Subtraction & addition equations (1 of 2)  e.g. a + 3 = 7 and x – 9 = 11 (From Worksheet)
• Subtraction & addition equations (2 of 2)  e.g. a + 3 = 7 and x – 9 = 11 (From Worksheet)
• Multiplication & division equations (1 of 2)  e.g. 3n = 12 and a/7 = 3 (From Worksheet)
• Multiplication & division equations (2 of 2)  e.g. 3n = 12 and a/7 = 3 (From Worksheet)
• Addition, subtraction, multiplication & division equations  (From Worksheet)
• Solving equations in two steps (1 of 4)  e.g. 5n + 4 = 29 (From Worksheet)
• Solving equations in two steps (2 of 4)  e.g. a/4 + 3 = 7 (From Worksheet)
• Solving equations in two steps (3 of 4)  e.g. 7n – 3 = 18 (From Worksheet)
• Solving equations in two steps (4 of 4)  e.g. b/9 – 4 = 6 (From Worksheet)

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Everything You Need to Know about the Inequality Word Problems Worksheet

Created on Mar 16, 2023

Updated on June 6, 2023

Inequalities are no fun for an average young learner. They’re even less fun when you throw a word problem into the mix. More often than not, learners may encounter a math question that looks somewhat like this:

Jake and Hannah were asked to take 850 baskets of apples to the farmer’s market. Jake took 200 more baskets than Hannah did.

Inequalities Problems Worksheets

Inequalities Word Problems Worksheet With Answers

Two Step Inequalities Word Problems Worksheets

Linear Inequalities Word Problems Worksheet Pdf

Solving Inequalities Word Problems Worksheet

Inequalities Word Problem Worksheet

Write an inequality to determine Y – the number of baskets that Hannah could have carried.

While this type of questions may seem easy at first glance, they typically require multiple steps to arrive at an accurate answer. For many students, this is where they lose the battle.

Fortunately, the inequalities word problems worksheet can help young learners overcome this hurdle. Let’s find out how.

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About the real world inequality problems worksheet.

The inequality problems worksheet is an excellent resource for any student looking to learn how the concept works. It contains a variety of exercises on inequality word problems designed to test the learner’s knowledge and push them towards new limits. First, a student will start off with simple problems, which gradually introduces them to the topic and eases them into a comfort zone.

As time goes on, they’ll begin to try out more challenging tasks, thus exercising their critical and logical reasoning skills. At the end of the day, they’ll have a firm grasp of inequality word problems and will be able to handle even the most complex exercises with ease.

Just like our other worksheets, the writing inequalities from word problems worksheet also comes with detailed solutions and answers to guide students along their learning journey.

Benefits of the Systems of Inequalities Word Problems Worksheets

The inequalities problems worksheets are an excellent addition to any student’s learning arsenal. The exercises from these worksheets are designed to equip a learner with analytical skills, speed, and accuracy. The skills derived from this worksheet are also transferable, which means that they can be transferred to other math topics or even other subjects as well.

Inequality Word Problems Worksheets PDF

Inequalities Word Problems Worksheet

Inequality Problems Worksheet

Inequality Word Problems Worksheet

Writing Inequalities From Word Problems Worksheet

As a seasoned educator with a Bachelor’s in Secondary Education and over three years of experience, I specialize in making mathematics accessible to students of all backgrounds through Brighterly. My expertise extends beyond teaching; I blog about innovative educational strategies and have a keen interest in child psychology and curriculum development. My approach is shaped by a belief in practical, real-life application of math, making learning both impactful and enjoyable.

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Inequality Word Problems

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Word Problems with inequalities

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Home » Worksheets » The Best Teacher-Approved Solving Inequalities Worksheets

The Best Teacher-Approved Solving Inequalities Worksheets

Are you looking for a high-quality worksheet on solving inequalities? If so, Teach Simple is the best starting point. Inequalities are a challenging topic in mathematics, particularly because there are statements where two unequal values. In solving inequalities, a student must look for all values of the variable that make the inequality true. It is a skill that takes time to learn, and that is where the inequalities worksheets come in.

At Teach Simple, we have professionals behind our worksheets. Our teaching materials follow the education standards of the USA, UK, Canada, and Australia, so you can be sure your students will learn government-approved content. All our learning materials are created by educational experts with several years of experience in the education sector. The materials are user-friendly, engaging, attractive, and effective.

Table of Contents

Things to look for when choosing worksheets for solving inequalities, examples of worksheets for solving inequalities, where can you find online inequalities worksheets, benefits of paid vs. free worksheets, why choose teach simple for your solving inequalities worksheet.

When you are looking for worksheets on solving inequalities, there are a few things that you will want to keep in mind, including:

Make sure the worksheets you choose are of high quality, meaning they should be well-written and free of errors. A worksheet with errors cannot help a student learn; it can only worsen their situation.

The students’ age

Make sure the worksheets are appropriate for the level of the students. Some worksheets are for kids in grades 1 and 2, while others are for students in grades 7 up to 12. You can’t give a very simple or very difficult worksheet to a student. This can make them lose interest in learning. Additionally, the worksheets should be interesting and engaging.

The worksheet you chose should be clear and concise. This is particularly important when dealing with word problems. The statements should be clear so a student can understand them and form the inequalities before graphing them. Furthermore, the worksheets should not be confusing but easy to understand and use.

Solving Inequalities – Leveled Checking Worksheet By Eight Gone Sideways

The leveled checking worksheet was designed by Eight Gone Sideways for grades 9, 10, 11, and 12. It has four sets (A, B, C, and D), each with three questions, and there is also an answer bank. The students are supposed to complete the problems in sets A and B and then match their solutions with what is on the answer bank.

Set C has proposed answers, and the students are supposed to determine whether the answers are correct or not. In the last set, the students are supposed to work through the problems and show their steps.

Solving 2-Step Inequalities MAZE Activity By The Math Cafe

Solving 2-Step Inequalities MAZE Activity is a fun worksheet for 7th-grade students. Authored by The Math Caf, these worksheets have word problems that lead to inequalities like px + q  r or px + q > r, where x is a variable and p and q are rational numbers.

The students are also required to graph their inequalities and interpret them in the context of the word problems. This resource has an optional workspace for students and answer keys.

Inequalities Task Cards By AlwaysLearning

Just as the name implies, these are printable task cards that you can print and laminate for durability. The cards are designed by AlwaysLearning and can be used by individual students or in a group setting with small groups, of course. The inequalities on the task cards are to be solved graphically, and there is an answer key and recording sheet.

Equations and Inequalities 6th Grade Worksheet By TheBrightestKid

This inequalities worksheet is designed for sixth-grade learners. The author, TheBrightestKid, included 19 pages of problems for the students to solve. After solving, the student will select matching solutions from a given set of solutions. And if their answers don’t match, they will have to identify their mistakes and rework the problems.

St. Patrick’s Day Inequities Activity By Have Fun Teaching

St. Patrick’s Day Inequalities Activity is an interactive worksheet created with grades 1 and 2 pupils in mind. The worksheet was created by Have Fun Teaching and is guaranteed to keep your kids busy. The worksheet dwells on numbers less than or greater than.

Graphing Inequalities in Two Variables (Spring) By Peter Jonnard

This resource comes in the form of Microsoft Word worksheets that you can download and print. You can use them with your students in grades 7, 8, and 9. These worksheets focus on the graphing of inequalities. The best part of it is that it comes with an answer key. Graphing Inequalities in Two Variables (Spring) is authored by Peter Jonnard.

Solving 1 and 2-Step Inequalities: Notes, Practice, and Partner Activity by The Math Cafe

The Solving 1 and 2-Step Inequalities worksheet is intended to teach grade 7 students number system standards. The sheets are to be used by pupils who already know how to solve 1- and 2-step linear equations.

Note that the sheets do not have instructions on solution steps, except for division by negative numbers. The Math Cafe created the sheets, which are excellent for teaching students how to work with word problems that lead to inequalities.

Systems of Inequalities: Guided Notes and Homework Set By Eddie McCarthy

Systems of Inequalities Guided Notes are created by Eddie McCarthy. There are five editable PDF files in this package. It also includes guided notes, an answer key, and homework.

If you are a math teacher in grades 9, 10, 11, and 12, these worksheets are for you. The sheets teach math skills, and the guide notes will allow them to learn the skills and apply them. The homework sheets aid in further understanding algebra.

Graphing Linear Inequalities: Guided Notes and Homework Set By Eddie McCarthy

Graphing Linear Inequalities: Guided Notes and Homework Set is created by Eddie McCarthy for grades 9–12 students. The worksheets are supposed to teach graphing of inequalities, and there are guide notes that make things very easy. This package also comes with an answer key and homework for further understanding of the topic.

Visit the Teach Simple website for the highest quality worksheets for solving inequalities. Some worksheets are available on other websites, but you have to check their quality before downloading and using them.

If you are looking for solving inequalities worksheets online, you will find quite a number of them, some free and some not. However, not all of these worksheets are created equal. Some are of much higher quality than others. In general, paid worksheets are better than free ones for various reasons.

Paid worksheets are of much higher quality than free ones because they are usually created by experienced educators who know how to create effective learning materials. The paid version also includes various problems for solving inequalities for your students to practice with. This can help them better understand the concept.

Paid worksheets will provide your students with extra practice. If your students are having difficulty understanding inequalities or need more practice to master them, using a paid worksheet is your best option. This can be especially helpful if you find that your students are struggling with particular types of problems.

Paid worksheets can help keep your child motivated because they are engaging and attractive.

The main reason why you should choose our worksheets for solving inequalities is that they are of the highest quality. This is because experienced educators create them. Our worksheets are also affordable. We believe that everyone should have access to high-quality educational resources. Teach Simple also offers a 100% satisfaction guarantee and an unlimited download subscription model. Once you subscribe to our site, you can download all the teaching materials you need.

Contact us today to learn more about our solving inequalities worksheet and how Teach Simple can help you achieve your goals.

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Diana R. has over 30 years of experience as a middle school teacher and college professor. She holds a Doctorate from the University of California and has spent 15 years as an academic professor and teacher in the sciences, health, medical, technology, and business fields

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Inequality Word Problems Worksheets

We use inequalities to compare two values. They give us an idea of relative size by stating that one is greater, lesser, equal, or not equal to the other value. Many times, when we use math, we do not need an exact answer, just an idea if something is going to work. I was reminded of this concept this very morning. I am a lacrosse coach and I have a bag that carries 80 lacrosse balls. There were already 28 balls in the bag and the school bought me a 50 pack of new balls. I had to quickly understand if that entire pack would fit in my bag. With the help of a quick inequality, I figured out there were too many for the bag. These worksheets and lessons help students learn how to write inequalities when given a word problem.

Aligned Standard: Grade 7 Expression & Equations - 7.EE.B.4b

• Amanda and Her Flowers Step-by-step Lesson - How many lilies can she afford? She wants to buy a pair of red rose flowers for $18 and spend the rest on lily flowers. Each lily flower costs $11. Write an inequality for the number of lily flowers she can purchase.
• Guided Lesson - Kimberly has $80. She wants to purchase a school bag for $16 and as many pairs of shoes as she can. Each pair of shoes is $8. Write an inequality for the number of school shoes she can purchase.
• Guided Lesson Explanation - Pay close attention to the graphing explanation it will save you time and time again.
• Practice Worksheet - This one may take students a lot time. Make sure to give them plenty of time and scrap paper.
• Matching Worksheet - If you are really good at writing and understanding inequalities, this will be a breeze for you.
• Applied Problems of Inequalities Five Worksheet Pack - I totally love these types of problems. Most people will call them riddles when they are just really calculated math.
• Triangular Inequalities Worksheet Five Pack - It is all about finding the longest side based on the measure of angles.
• Answer Keys - These are for all the unlocked materials above.

Homework Sheets

We start students off with the word problems and then we move to number lines.

• Homework 1 - Jacob gives his son $30 for chocolate. His son spends $16 on dark chocolate and spends the rest on white chocolate. Each white chocolate costs $7. Write an inequality for the number of white chocolate he can purchase.
• Homework 2 - Solve -0.3x – 4 > -9.4 and graph the solution on a number line.
• Homework 3 - Sarah has $80. She wants to purchase a school bag for $16 and as many pairs of shoes as she can. Each pair of shoes is $8. Write an inequality to find how many pairs of shoes she can purchase.

Practice Worksheets

The biggest problem here is for students to remember the difference between an open and closed inline arrow.

• Practice 1 - Solve 2x + 2 > 4 and graph the solution on a number line.
• Practice 2 - Brock has $23 to spend on cupcakes. He wants to buy an orange cupcake for $8 and spend the rest on pink cupcakes. Each pink cupcake costs $5. Write an inequality that can be used to determine the number of pink cupcakes Brock can buy.
• Practice 3 - Mary has $20 to spend. She buys lunch for $14 and spends the rest on banana biscuits. Each banana biscuit costs $3. How many banana biscuits did she buy?

Math Skill Quizzes

I couldn't fit any number line based questions in here, sorry!

• Quiz 1 - Margaret wants to purchase a caramel apple ($7) and water melon slice ($4). She spends the rest of her money on pizza. She has $19 to start. Each pizza costs $2. How many pizzas can she get?
• Quiz 2 - Aiden wants to buy some clothes for his birthday. He has $40. He purchases a white shirt for $14. He spends the rest of the money on black pants. Each pair of pants costs $8. Write an inequality for the number of pairs of pants he can purchase.
• Quiz 3 - Brooke goes to the market. She purchases a red rose flower for $10 and a lily for $8. She spends the rest of her money on white roses. She has $30 at the start. Each white rose costs $3. How many white roses can she get?

How to Write Word Problems as Inequalities

Do you feel like algebraic word problems are difficult? Don't worry; we'll help to make these word problems as easy as possible. The first and foremost, you need to follow a few steps that will help you solve algebraic word problems. If you stay consistent with this, it will become a habit quickly. Here are some habits you should get in when working with these types of problems:

Step 1) Slow Down and Focus - Read the entire problem thoroughly. Highlight important information and keywords that you think are needed to solve the problem. Those keywords will often present themselves as math operations and comparisons that will help us form and ultimately write our inequality.

Step 2) Determine the Present Conditions - Carefully identify the variables. If there are any values such as coefficients or constants make sure to state those as well. I find it helpful to create an itemized list of all of them and the values associated with them before going any further.

Step 3) Create an Inequality - Take your itemized list and then look for keywords that may indicate relationships between these elements. Some of the phrases you are looking for include:

at least – this indicates a relationship that can be defined as greater than or equal. We use this symbol to signify this: (≥)

less, lesser, less than – indicates a less than (<) relationship.

bigger, larger, or more than – signifies a greater than (>) relationship.

no more than - this indicates a relationship that can be defined as less than or equal. We use this symbol to signify this: (≤)

Once we understand the statement made by the inequality, we place the variable that indicates the condition that needs to be satisfied on one side of the comparison symbol and we arrange the remaining variables and constants on the other side, as stated in the word problem.

Step 4) Solve It For Missing Parts - You can rearrange an inequality much like an equation to solve for a variable. Just consider the compare symbol an equals symbol. Once you have your final answer, realize that inequalities do not give us an exact location of the solution, rather an idea of where the answer lies. Recheck and justify your answer. You can do this by seeing if a fixed value would satisfy the situation that is presented.

In a saving account, Sam deposited $400. She wants to have at least $100 in her account by the end of summer. She withdraws $15 every week for food and movie tickets.

Here is how you will write an inequality: First, make sure you highlight the keyword (at least), that will be written down within the inequality as a (≥). Thoroughly read and highlight any other information that you need when writing the inequality. We can identify that she starts with $400 and in the end needs to have $100 or more. We can then identify that every week $15 is being removed from the total. We can rewrite that as 15w, where w is equal to the number of weeks. Here, the variable is the number of weeks since that is what you don't know. Now generating the inequality will be easy; 400 - 15w ≥ 100. We can solve for the number of weeks through these steps:

400 - 15w ≥ 100 (Subtract 400 from both sides)

- 15w ≥ -300 (Divide by -15)

This tells us that Sam can live on this budget for 20 weeks.

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INEQUALITY WORD PROBLEMS WORKSHEET

Problem 1 : 

Sum of a number and 5 is less than -12. Find the number.

Problem 2 : 

David has scored 110 points in the first level of a game. To play the third level, he needs more than 250 points. To play third level, how many points should he score in the second level ?

Problem 3 : 

An employer recruits experienced (x) and fresh workmen (y) for his firm under the condition that he cannot employ more then 9 people. If 5 freshmen are recruited, how many experienced men have to be recruited ? 

Problem 4 : 

On the average, experienced person does 5 units of work while a fresh one (y) does 3 units of work daily. But the employer has to maintain an output of at least 30 units of work per day. How can this situation be expressed ? 

Let x be the number.

Step 1 : 

Write the inequality.

x + 5 < -12

Solve the inequality using Subtraction Property of Inequality.

Subtract 5 on from both sides. 

(x + 5) - 5 < -12 - 5

So, the number is any value less than -17. 

Let x be points scored in the second level.

He has already had 110 points in the first level.  

Points scored scored in the second level  =  x

Total points in the first two levels  =  x + 110

To play third level, the total points in the first two levels should be more than 250. So, we have

x + 110 > 250 

Subtract 110 on from both sides. 

(x + 110) - 110 > 250 - 110

So, he has to score more than 140 points in the second level. 

Write the inequality. 

x + y ≤ 9

Substitute 5 for y.

x + 5 ≤ 9

Subtract 5 from both sides.

(x + 5) - 5 ≤ 9 - 5

To meet the given condition, no. of freshmen to be recruited can be less than or equal to 4. 

On the average, experienced person does 5 units of work while a fresh one (y) does 3 units of work daily. But the employer has to maintain an output of at least 30 units of work per day. How can this situation be expressed ?

Let x and y be the number of experienced person and fresh workmen respectively. 

From the given information, we have

Total number of units of work done by experienced person per day is 

Total number of units of work done by fresh one per day is

=  3y 

Total number of units of work done by both experienced person and fresh one per day is

=  5x + 3y 

As per the question, total number of units of work per day should be at least 30 units.  That is, total number of units of work (5x+3y) should be equal to 30 or more than 30.  So, we have 5x + 3y ≥ 30.

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Multi Step Inequalities Word Problems Part 1 - NO PREP Printable Worksheet

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Description

Master Multi Step Inequalities through Real-World Modeling

Transform your students into masters of Multi Step inequalities with Variables on One Side using this comprehensive "Multi Step Inequalities Word Problems" printable PDF worksheet. This NO PREP printable resource offers carefully crafted word problems that bridge theoretical understanding with real-world application.

Key Features:

1. Diverse Word Problems: The worksheet includes 12 meticulously designed word problems, each presenting a unique challenge for students to model and solve using Multi Step inequalities.

2. Multiple Formats: With various printable versions (all-in-one, work-showing, organized boxes), this resource is adaptable to different teaching preferences and student needs, catering to in-class assignments, homework, quizzes, or exams.

3. Curated Database: Save valuable time searching for relevant problems. Backed by a curated database, these word problems are diverse and of high quality, ensuring students are exposed to a range of scenarios that reinforce understanding.

4. Real-World Scenarios: By connecting abstract concepts with practical applications, students will strengthen their critical thinking skills while mastering the art of modeling and solving Multi Step inequalities in authentic situations.

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Answer Key:

https://www.teacherspayteachers.com/Product/Linear-Inequalities-Word-Problems-NO-PREP-Printable-Worksheet-w-Answer-Key-10481392

https://www.teacherspayteachers.com/Product/Linear-Inequalities-Word-Problems-Part-1-NO-PREP-w-Step-by-Step-Solutions-10960507

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SOLVING LINEAR INEQUALITIES WORD PROBLEMS IN TWO VARIABLES

A statement involving the symbols ‘>’, ‘<’, ‘ ≥’, ‘≤’ is called an inequality. 

By understanding the real situation, we have to use two variables to represent each quantities

Problem 1 :

Katie has $50 in a savings account at the beginning of the summer. She wants to have at least $20 in the account by the end of the summer. She withdraws $2 each week for food, clothes, and movie tickets. Write an inequality that expresses Katie’s situation and display it on the graph below. For how many weeks can Katie withdraw money?

Let x be the number of weeks 

50 - 2x  ≥  20

2x  ≤  30

x  ≤  15 weeks

Problem 2 :

Skate Land charges a $50 flat fee for a birthday party rental and $4 for each person. Joann has no more than $100 to budget for her party. Write an inequality that models her situation and display it on the graph below. How many people can attend Joann's party.

Assume x people can attend the party.

y = 50 + 4x

50 + 4x ≤ 100

So, 12 people can attend Joan’s party.

Problem 3 :

Sarah is selling bracelets and earrings to make money for summer vacation. The bracelets cost $2 and the earrings cost $3. She needs to make at least $60. Sarah knows she will sell more than 10 bracelets. Write inequalities to represent the income from jewelry sold and number of bracelets sold. Find two possible solutions.

Let x be the number of bracelets sold.

Let y be the number of earrings sold.

2x + 3y ≥ 60

If x = 11, then 2(11) + 3y  ≥ 60

3y  ≥ 60 - 22

3y  ≥ 38

Since y is the number of earrings, x = 11 is not possible.

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