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## Two-Step Equations

Two step equations are equations that can be solved within exactly two steps. Two step equations are extremely easy to solve. As the name suggests, two step equations take only two steps to solve. These equations are just a little complicated than the one step equations. While solving a two step equation, we need to perform the operation on both sides of the equals to sign.

In this article, we will understand the meaning of two step equations with integers, decimals, and fractions, how to solve them, the golden rule to solve two step equations along with some examples for a better understanding.

## What are Two Step Equations?

Two step equations are algebraic problems that take just two steps to solve. The two step equation is a linear equation in one variable . While performing an operation for solving a two step equation, we need to perform the same operation on both sides of the equation. We isolate the variable on one side of the equation to determine its value.

## Two Step Equations Definition

Two step equations are algebraic equations and are the equations that can be solved in exactly two steps and gives the final value of the variable in two steps. Generally, two step equations are of the form ax + b = c, where a, b, c are real numbers. A few examples of two step equations are:

• 0.3y + 5 = 1
• (2/3)z - 12 = 10

## Solving Two Step Equations

Two step equations are very easy to solve. It includes just one extra step as compared to one-step equations to solve. We can solve a two-step equation by isolating the variable (usually represented by an alphabet or letter) on one side of the equation and all other values on the other side. The general two steps to solve the two-step equations are:

• Step 1: Addition and subtraction to isolate the variable.
• Step 2: Multiplication  or division  to determine the value of the variable.

Let us consider a few examples and solve two-step equations to understand the concept of solving two-step equations.

Example 1: Solve the equation 2x + 6 = 12.

To solve the two step equation 2x + 6 = 12, we need to determine the value of x. Let us solve it step-wise.

Step 1: Subtract -6 from both sides of the equation to isolate the variable x.

2x + 6 - 6 = 12 - 6

Step 2: Divide both sides of the equation by 2 to solve for x.

Hence, we have solved the equation 2x + 3 = 12 in just two steps.

Thus the two-step equation can be easily solved in a sequence of steps, as presented above.

## Two-Step Equations with Decimals and Fractions

Two step equations that have decimals and fractions as the coefficient of the variable and constant term are said to be two step equations with decimals and fractions. A few examples of two step equations with fractions and decimals are:

• 0.3 x + 2/3 = 1
• 3x - 0.5 = 1.2
• (1/3) x + 4/5 = 3/4

These equations are solved in the same manner as the general two steps equations and the same steps are followed to determine the value of the variable.

## Golden Rule to Solve Two Step Equations

The golden rule to solve two step equations is to perform all operations simultaneously on both sides of the equation. To isolate the variable on one side of the equation and to determine its value, we first add or subtract on both sides of the equation and then multiply or divide on both sides to get the final solution of the two step equation.

Important Notes on Two Step Equations

• Remove the parentheses and combine like terms to simplify each side of the two-step equation.
• Always remove the constant first by adding or subtracting the appropriate number.
• Always verify the solution in the end.

Topics Related to Two Step Equations

• Equations in Math
• Simple equations
• Algebraic formulas

## Two Step Equations Examples

Example 1: Solve the two step equation (x/6) - 7 = 11

Solution: To solve the given two step equation, we will follow the steps discussed above in the article.

Step 1: Add 7 to both sides of the given two step equation

(x/6) - 7 + 7 = 11 + 7

⇒ (x/6) = 18

Step 2: Multiply both sides of the equation by 6.

6 × x/6 = 6 × 18

Answer: Hence the solution to the given two step equation (x/6) - 7 = 11 is x = 108.

Example 2: Determine the solution of the two step equation (2/3) z + 0.8 = 1.5

Step 1: Subtract 0.8 from both sides of the given two step equation

(2/3) z + 0.8 - 0.8 = 1.5 - 0.8

⇒ (2/3) z = 0.7

Step 2: Multiply both sides of the equation by (3/2).

(3/2) × (2/3) z = (3/2) × 0.7

Answer: Hence the solution to the given two step equation (2/3) z + 0.8 = 1.5 is x = 1.05

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## Practice Questions on Two Step Equations

Faqs on two step equations, what are two step equations in algebra.

Two step equations are algebraic equations that take just two steps to solve.First, the variable is isolated by adding or subtracting a numeric value on both sides of the equation. Secondly, the value of the variable is computed by multiplying or dividing the variable by an appropriate number.

## What are the Steps to Solve Two Step Equations?

The general two steps to solve two step equations are:

• Step 1: Simplify the given equation by removing all brackets and parenthesis:
• Step 2: Add or subtract to isolate the variable.
• Step 2: Multiply or divide to determine the value of the variable.
• Step: Verify the answer by substituting it in the given equation .

## How to Solve Two Step Equations?

Two step equations can be solved by following two quick steps:

• Step 1: Add or subtract numbers on either sides, to isolate the variable.

## IS Two Step Equation the Same as A Multi-Step Equation?

Two-step equation can also be called a multi-step equation since it involves more than one step. And a multi-step equation can have two or more steps, in the process of solving the equation.

## What is the Difference Between One Step and Two Step Equations?

One step equations take just one step to solve whereas two steps equations take two steps to get to the solution. Two-step equations include just one extra step as compared to one step equations to solve.

## What is the Goal of Solving Two Step Equations?

The goal of solving two step equations is to isolate the variable and determine the value of the variable. And in the end, the variable should satisfy the given two step equation.

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## How to Solve Two Step Algebraic Equations

Last Updated: May 10, 2023 Fact Checked

This article was reviewed by Grace Imson, MA . Grace Imson is a math teacher with over 40 years of teaching experience. Grace is currently a math instructor at the City College of San Francisco and was previously in the Math Department at Saint Louis University. She has taught math at the elementary, middle, high school, and college levels. She has an MA in Education, specializing in Administration and Supervision from Saint Louis University. This article has been fact-checked, ensuring the accuracy of any cited facts and confirming the authority of its sources. This article has been viewed 750,292 times.

Two step algebraic equations are relatively quick and easy -- after all, they should only take two steps. To solve a two step algebraic equation, all you have to do is isolate the variable by using either addition, subtraction, multiplication, or division. If you want to know how to solve two step algebraic equations in a variety of ways, just follow these steps.

## Solving Equations with One Variable

Remember the Golden Rule of Algebra. Whatever you do to one side of an equation must be done to the other side to maintain the balance. That is why 7 is subtracted from the 15 as well. We only need to subtract 7 once per side, which is why the 7 is not subtracted from the -4x as well.

• -4x + 7 = 15 =

Again, whatever you do to the equation must be done to both sides. That is why you see ÷ -4 twice.

## Solving Equations with One Variable on Each Side

• Adding +3 to the left side of the equation, -2x -3, will give you (-2x -3) + 3, or -2x on the left side.
• Adding +3 to the right side of the equation, 4x -15, will give you (4x - 15) +3, or 4x -12.
• Therefore, (-2x - 3) +3 = (4x - 15) +3 = -2x = 4x - 12
• The new equation should read -2x = 4x -12

• -2x - 4x = (4x - 12) - 4x = -6x = -12

• -6x ÷ -6 = -12 ÷ -6

## Other Ways to Solve Two-Step Equations

• 11 = 3 - 7x =
• 11 - 3 = 3 - 3 - 7x =
• 8/-7 = -7/7x
• -8/7 = x or -1.14 = x

• x/5 + 7 = -3 =
• (x/5 + 7) - 7 = -3 - 7 =
• x/5 * 5 = -10 * 5

## Community Q&A

• When multiplying or dividing two numbers with different signs, (i.e., one positive & the other negative) the result is always negative. If both signs matched, then the solution would be a positive number. Thanks Helpful 1 Not Helpful 1
• If there is no number in front of the x , assume it is a 1x. Thanks Helpful 0 Not Helpful 0

## You Might Also Like

• ↑ https://www.registerednursing.org/teas/solving-equations-one-variable/
• ↑ https://www.chilimath.com/lessons/intermediate-algebra/solving-two-step-equations/
• ↑ https://virtualnerd.com/middle-math/equations-functions/solving-two-step/practice-solve-two-step-equation
• ↑ https://flexbooks.ck12.org/cbook/ck-12-interactive-middle-school-math-7-for-ccss/section/3.7/primary/lesson/solving-two-step-equations-4424709-msm7-ccss/

To solve two step algebraic equations with a variable on 1 side, start by using addition or subtraction to isolate the variable term. For example, if the equation is 4x + 7 = 15, isolate 4x by subtracting 7 from both sides, so that the equation becomes 4x = 8. Next, divide 4x by the number in front of the variable, so that you are left with only x. Finally, divide the other side by the same number to get x = 2. To learn more, including how to solve algebraic equations with a variable on both sides, scroll down. Did this summary help you? Yes No

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## Two-step word problems

Here you will learn about two-step word problems, including how to solve a two-step word problem, how to represent these problems using equations, and how to assess the reasonableness of answers.

Students will first learn about two-step word problems as part of operations and algebraic thinking in 3 rd grade and will continue using this skill throughout elementary and middle school.

## What are two-step word problems?

Two-step word problems are word problems or story problems that require two steps to find the answer. These two steps can involve the same operation or two different operations.

To solve a two-step word problem, you must read the problem carefully before identifying each of the two steps. After identifying the two steps, you can write an equation for each step. Then you will need to solve each equation in order before arriving at the final answer.

For example,

Sarah had \$15. She spent \$8 on a new book. Then her mom gave her \$5. How much money does she have now? We can break down the problem into steps and write an equation. Sarah starts with \$15, so this is the starting number.

Then she spends \$8 on a new book. This means you need to subtract \$8. This is step one .

x represents the amount of money Sarah has after buying the book.

Next, Sarah receives \$5 from her mom. This needs to be added to the remaining amount from step one. This is step two . t represents the total of money Sarah has after her mom gave her \$5 .

Chris has \$247.50 left from his paycheck. To estimate the amount of Chris’s paycheck, you can multiply 12 by 25. You could also multiply 12 by 30, but note this will be a high estimate. 12 \times 25=300-65 = \$235 which makes \$247.50 a reasonable answer. ## Example 5: interpreting remainders in two-step division word problem Five 5 th grade classes each have 24 students and 2 teachers attending a field trip. Each bus can hold 48 people. How many buses are needed to carry all of the students and teachers to the field trip? First, you need to find out how many students and teachers are attending the field trip altogether. To do this, you will need to multiply 5 \times 26. 5 \times 26=x Next, you need to divide the total number of people by the number of people each bus can carry. x \div 48=b Now that you have identified the steps, you can solve the equations in order. For this problem, you will need to refer back to the question in order to interpret the remainder. It asks: How many buses are needed to carry all of the students and teachers to the field trip? So in this word problem, the answer 2 \; R \, 34 represents 2 full buses with 34 people leftover. Since those 34 people also need a bus to ride to the field trip, you would round up the answer to 3 so that all people can attend the field trip. 3 buses are needed to carry all of the students and teachers to the field trip. There are about 125 people attending the field trip (about 25 people \times 5 classes) and about 50 people can fit on a bus. 125 \div 50=2.5, so the answer of 3 buses is reasonable. ## Example 6: interpreting remainders in two-step division word problems Haruki had 39 books. He got 7 more books for his birthday. His bookshelf has 4 shelves. He wants to put the same number of books on each shelf and put the remaining books on top of his bookshelf. How many books will go on top of Haruki’s bookshelf? First, you need to determine how many books Haruki has altogether. So step 1 is to add to find the total number of books. Next, you will need to divide the total number of books by the number of shelves Haruki has. For this problem, you will need to refer back to the question in order to interpret the remainder. It asks: How many books will go on top of Haruki’s bookshelf? So in this word problem, the remainder is your answer. 2 books will go on top of Haruki’s bookshelf. Haruki has about 45 books that he wants to divide equally between 4 shelves, which means there would be about 11 books on each shelf with about 1 left over. So the answer of 2 books is reasonable. ## Teaching tips for two-step word problems • Begin with simple 2 -step word problems on math worksheets that involve familiar situations and basic operations. Gradually increase the complexity as learners gain confidence and understanding. • Lesson plans should involve step-by-step problem-solving strategies, such as underlining important information, identifying keywords, and breaking the problem into smaller parts. Model how to solve each step before tackling the problem as a whole. • Connect math word problems to real-life scenarios that are relevant and interesting to students. This can help them see the practical application of math and reasoning skills and increase engagement on word problem worksheets. • Provide students with a template if needed to help them break down the problem into steps. You can also provide students with a printable answer key to check their work. If their answers do not match, they can go back to investigate and find the correct steps. • Start with simple two-step word problems with 1 -digit numbers to allow students to focus on identifying the two steps. Then advance to 2 -digit and 3 -digit problems. ## Easy mistakes to make • Incorrect order of operations Students might perform operations in the wrong order, leading to incorrect solutions. It is imperative that students write their equations correctly to ensure the operations are performed in the correct order. • Not checking the solution Sometimes, students may not take the time to review their solution to ensure it makes sense in the context of the problem. Checking the answer against the problem statement or using estimation to verify reasonableness can help catch errors. • Missing a step or performing the steps in the wrong order Sometimes, students may misinterpret the problem statement, causing them to miss a step or mix up the order of steps. It’s crucial to carefully read and understand what the problem is asking for before attempting to solve it. ## Related arithmetic lessons • Skip counting • Number sense • Inverse operations • Money word problems • Calculator skills ## Practice two-step word problem questions 1. Frankie has \$287 in her checking account. She spent \$56 on her phone bill and then spent \$39 at dinner. How much money is left in her account?

This is a two-step subtraction word problem, meaning each of the two steps involves subtraction.

1 st step: Subtract the amount spent on the phone bill.

2 nd step: Subtract the amount spent at dinner from what is left after step 1.

2. Elliot has 145 marbles in his collection. He lost 18 marbles and then bought 27 more. How many marbles does he have now?

154 marbles

190 marbles

136 marbles

100 marbles

This two-step word problem involves two different operations.

1 st step: Subtract the number of marbles Elliot lost.

2 nd step: Add the number of marbles Elliot bought to the total remaining marbles from step 1.

127 + 27 = 154 marbles

3. Mrs. Smith baked 24 cookies in the morning and 18 cookies in the afternoon. If she wants to pack them into bags of 6 cookies each, how many bags of cookies will she have in total?

1 st step: Find the total number of cookies Mrs. Smith baked.

2 nd step: Divide the total number of cookies by the number of cookies per bag to find the total number of bags.

42 \div 6=7 bags

4. Sarah has 15 comic books. She decides to buy 5 more comic books at the store. Each comic book costs \$3.50. If she also buys a poster for \$8, how much money will Sarah spend in total?

This two-step word problem involves two different operations. Also note that there is an extra bit of unnecessary information in the word problem (Sarah has 15 comic books).

1 st step: Determine the total cost of the comic books Sarah buys.

2 nd step: Add the amount spent on the poster to the total from step 1.

5. Libby is selling boxes of cookies for a fundraiser at her school. So far, she has sold 29 boxes of cookies for \$12 each. If she has a goal of raising \$400, how much more money does she need to earn?

1 st step: Multiply to find the amount Libby earned from selling 29 boxes of cookies.

2 nd step: Determine how much more money Libby needs to earn to reach her goal by subtracting the total from step 1 from her goal amount.

6. Georgio has 128 complete fossils in his collection. He donated 19 fossils to a local museum. He wants to arrange the rest of his fossils in a display case in his house. The display case has 7 shelves. If he wants to put the same number of fossils on each shelf, how many will go on each shelf?

1 st step: Subtract to find the number of fossils remaining after donating to the museum.

2 nd step: Determine how many fossils Georgio can put on each shelf by dividing the remaining fossils by the number of shelves.

## Two-step word problems FAQs

To solve a two-step word problem, you must read the problem carefully before identifying each of the two steps. After identifying the two steps, you can write an equation. Then you will need to perform each step in the correct order before arriving at the final answer.

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• Two-step equations – word problems

Simply put, two-step equations – word problems are two step equations expressed using words instead of just numbers and mathematical symbols. They are just a bit more complicated than one-step equations with word problems and they demand just a bit more effort to solve. If you are not confident in your abilities to solve two-step equations with word problems, you can go to one-step equations – word problems and practice some more before continuing with this lesson. But if you feel ready, we will show you how to solve it using this example:

Hermione’s Bikes rents bikes for $10 plus$4per hour. Janice paid $30 to rent a bike. For how many hours did she rent the bike? First thing we have to do in this assignment is to find the variable and see what its connection is with the other values. The thing we do not know is the number of hours Janice rented the bike for and we have been asked to find that out. That means the number of hours is our variable. The cost of renting a bike is 10$ to take the bike and 4$for every hour it spends in our possession. The final sum Janice paid is$30. Let us write that down as an equation.

4 * x + 10 = 30

Now, in order to make things neater and more clear, let us move all the numbers (except for the number 4 – we have to get rid of it in a different way) to the right side of the equation. Like this:

4 * x = 30 – 10

To simplify things further, let us perform the subtraction.

The next thing to do is to get rid of the number 4 in front of the variable. We will do that by dividing the whole equation by 4.

4 * x = 20 |:4

Now that we have calculated the value of the variable, we can tell that Janice rented that bike for 5 hours. If you want to check the result – you can. If you multiply $4 that Janice paid per hour by the 5 hours she spend with that bike and then add the$10 she had to pay regardless of the time she spent with the bike, you will get a total sum of $30 that is indeed the full sum she paid. These word problems are called two-step because you have to perform two mathematical operations in order to solve them. In this case – addition (subtraction) and multiplication (division). To practice solving two-step equations – word problems, feel free to use the worksheets below. ## Two-step equations – word problems exams for teachers Two-step equations – word problems worksheets for students. ## Basic Mathematical Operations • Addition and subtraction • Multiplying • Divisibility and factors • Order of operations • Greatest common factor • Least common multiple • Squares and square roots • Naming decimal places • Write numbers with words • Verbal expressions in algebra • Rounding numbers • Convert percents, decimals and fractions • Simplifying numerical fractions • Proportions and similarity • Calculating percents • The Pythagorean theorem • Quadrilaterals • Solid figures • One-step equations • One-step equations – word problems • Two-step equations • Multi-step equations • Multiplying polynomials • Inequalities • One-step inequalities • Two-step inequalities • Multi-step inequalities • Coordinates • Graphing linear equations • The distance formula ## Linear Equations • Writing a linear equation • Systems of linear equations • Linear systems – word problems ## Recent Posts • Custom Math Writing Services – How Do They Help? Free Math Worksheets © 2024. All Rights Reserved. Free Math Worksheets is a math related website that contains pre-algebra, algebra and geometry worksheets and tests. Now, professors and teacher can reduce cheating by selecting printable exams to the individual students. Contact Us Please ensure that your password is at least 8 characters and contains each of the following: • a special character: @$#!%*?&

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## Course: 3rd grade   >   Unit 8

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The general two steps to solve two step equations are: Step 1: Simplify the given equation by removing all brackets and parenthesis: Step 2: Add or subtract to isolate the variable. Step 2: Multiply or divide to determine the value of the variable. Step: Verify the answer by substituting it in the given equation.

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The USUAL way of solving a two-step equation: Note: This is the "usual" method because most of the two-step equations are solved this way.Notice that Step 2 can alternatively be replaced by Step 3 which are the same essentially. 1) First, add or subtract both sides of the linear equation by the same number. 2) Secondly, multiply or divide both sides of the linear equation by the same number.

7. Multi-step equations review (article)

Step 1: Multiply the denominators (x/3) Step 2: Cross multiply the numerators and denominators (2x1 and 3x1) Step 3: Add the two products together (2x1=2, 3x1=3 therefore, add 2+3). WITHOUT touching the denominator! Step 4: 5/3b + 5 = 20. Subtract 5 from both sides of the equation to cancel out 5.

8. Two-step equations review (article)

5 years ago. The answer is c = 1. You would first combine all the like terms in the parenthesis. The only like terms are -5 and 6. The sum of those numbers gets you 1, then by subtracting 1 from both sides you are left with c = 1. You can even check it by putting 1 in c's place: 2= (1-5+6). 10 comments.

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10. Worked example: two-step equations

Worked example: two-step equations. Google Classroom. Microsoft Teams. About. Transcript. Sal solves the equation -16 = x/4 + 2. It takes two steps because he first has to subtract 2 from both sides and then multiply both sides by 4. Created by Sal Khan and Monterey Institute for Technology and Education. Questions.

11. Solving Two-Step Equations

Do you want to learn how to solve two-step equations in algebra? Watch this video by Mr. J, who will explain the steps and examples in a clear and engaging way. Whether you are a beginner or a ...

12. 3 Ways to Solve Two Step Algebraic Equations

1. Write the problem. The first step to solving a two step algebraic equation is just to write the problem so you can start to visualize the solution. Let's say we're working with the following problem: -4x + 7 = 15. [1] 2. Decide whether to use addition or subtraction to isolate the variable term.

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14. Algebra Basics: Solving 2-Step Equations

There was a confusing example in the original video. This is the updated version.This video shows students how to solve 2-step Algebra equations involving on...

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The Algebra Calculator is a versatile online tool designed to simplify algebraic problem-solving for users of all levels. Here's how to make the most of it: Begin by typing your algebraic expression into the above input field, or scanning the problem with your camera. After entering the equation, click the 'Go' button to generate instant solutions.

18. Two-Step Equations Practice Problems with Answers

Two-Step Equations Practice Problems with Answers. Hone your skills in solving two-step equations because it will serve as your foundation when solving multi-step equations. I prepared eight (8) two-step equations problems with complete solutions to get you rolling. My advice is for you to solve them by hand using a pencil or pen and paper.

19. Two Step Word Problems

Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. ... Begin with simple 2 -step word problems on math worksheets that involve familiar ...

20. Math Equation Solver

You can solve multiplication and division during the same step in the math problem: after solving for parentheses, exponents and radicals and before adding and subtracting. Proceed from left to right for multiplication and division. Solve addition and subtraction last after parentheses, exponents, roots and multiplying/dividing.

21. 2-step word problems (practice)

2-step word problems. The cash register at the ice cream store started the day with $120 . During the day, the store earned$ 56 selling ice cream. The manager also paid for a delivery out of the cash register. At the end of the day, the cash register had \$ 141 . How much did the delivery cost?

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23. Two-step equations

555.5 kB. 15078. September 3, 2019. Simply put, two-step equations - word problems are two step equations expressed using words instead of just numbers and mathematical symbols. They are just a bit more complicated than one-step word problems and they demand just a bit more effort to solve.

24. Two-step equations

13=2m+5‍. m=‍. Your answer should be. an integer, like 6‍. a simplified properfraction, like 3/5‍. a simplified improperfraction, like 7/4‍. a mixed number, like 1 3/4‍. an exactdecimal, like 0.75‍. a multiple of pi, like 12 pi‍ or 2/3 pi‍.

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26. Setting up 2-step word problems (video)

When you have a number in parenthesis next to another number, it means you have to multiply. If you have an expression in parenthesis, it means that you have to do that expression first in the overall equation. All in all, parenthesis are an essential part of math. Hope this helps. Have a great day! 😁.

27. 2<12

2<12. The Algebra Calculator is a versatile online tool designed to simplify algebraic problem-solving for users of all levels. Here's how to make the most of it: Begin by typing your algebraic expression into the above input field, or scanning the problem with your camera. After entering the equation, click the 'Go' button to generate instant ...