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Unit 2: Solving equations & inequalities
About this unit.
There are lots of strategies we can use to solve equations. Let's explore some different ways to solve equations and inequalities. We'll also see what it takes for an equation to have no solution, or infinite solutions.
Linear equations with variables on both sides
- Why we do the same thing to both sides: Variable on both sides (Opens a modal)
- Intro to equations with variables on both sides (Opens a modal)
- Equations with variables on both sides: 20-7x=6x-6 (Opens a modal)
- Equation with variables on both sides: fractions (Opens a modal)
- Equation with the variable in the denominator (Opens a modal)
- Equations with variables on both sides Get 3 of 4 questions to level up!
- Equations with variables on both sides: decimals & fractions Get 3 of 4 questions to level up!
Linear equations with parentheses
- Equations with parentheses (Opens a modal)
- Reasoning with linear equations (Opens a modal)
- Multi-step equations review (Opens a modal)
- Equations with parentheses Get 3 of 4 questions to level up!
- Equations with parentheses: decimals & fractions Get 3 of 4 questions to level up!
- Reasoning with linear equations Get 3 of 4 questions to level up!
Analyzing the number of solutions to linear equations
- Number of solutions to equations (Opens a modal)
- Worked example: number of solutions to equations (Opens a modal)
- Creating an equation with no solutions (Opens a modal)
- Creating an equation with infinitely many solutions (Opens a modal)
- Number of solutions to equations Get 3 of 4 questions to level up!
- Number of solutions to equations challenge Get 3 of 4 questions to level up!
Linear equations with unknown coefficients
- Linear equations with unknown coefficients (Opens a modal)
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- Linear equations with unknown coefficients Get 3 of 4 questions to level up!
Multi-step inequalities
- Inequalities with variables on both sides (Opens a modal)
- Inequalities with variables on both sides (with parentheses) (Opens a modal)
- Multi-step inequalities (Opens a modal)
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- Multi-step linear inequalities Get 3 of 4 questions to level up!
- Using inequalities to solve problems Get 3 of 4 questions to level up!
Compound inequalities
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- Compound inequalities: AND (Opens a modal)
- A compound inequality with no solution (Opens a modal)
- Double inequalities (Opens a modal)
- Compound inequalities examples (Opens a modal)
- Compound inequalities review (Opens a modal)
- Solving equations & inequalities: FAQ (Opens a modal)
- Compound inequalities Get 3 of 4 questions to level up!
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How to Solve a Problem
Last Updated: April 3, 2023 Fact Checked
This article was co-authored by Rachel Clissold . Rachel Clissold is a Life Coach and Consultant in Sydney, Australia. With over six years of coaching experience and over 17 years of corporate training, Rachel specializes in helping business leaders move through internal roadblocks, gain more freedom and clarity, and optimize their company’s efficiency and productivity. Rachel uses a wide range of techniques including coaching, intuitive guidance, neuro-linguistic programming, and holistic biohacking to help clients overcome fear, break through limitations, and bring their epic visions to life. Rachel is an acclaimed Reiki Master Practitioner, Qualified practitioner in NLP, EFT, Hypnosis & Past Life Regression. She has created events with up to 500 people around Australia, United Kingdom, Bali, and Costa Rica. There are 12 references cited in this article, which can be found at the bottom of the page. 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 1,314,945 times.
How you deal with challenges will often determine your success and happiness. If you’re stuck on how to solve a problem, try defining it and breaking it into smaller pieces. Choose whether to approach the problem logically or whether you should think about how the outcome might make you feel. Find ways to creatively approach your problems by working with other people and approaching the problem from a different perspective.
Approaching the Problem
- For example, if your room is constantly messy, the problem might not be that you’re a messy person. It might be that you lack containers or places to put your items in an organized way.
- Try to be as clear and thorough as possible when defining the problem. If it is a personal issue, be honest with yourself as to the causes of the problem. If it is a logistics problem, determine exactly where and when the problem occurs.
- Determine whether the problem is real or self-created. Do you need to solve this problem or is this about something you want? Putting things in perspective can help you navigate the problem-solving process.
- For example, you might have several problems to solve and need to decide which ones to tackle first. Solving one problem may ease tension or take stress off of another problem.
- Once you make a decision, don’t doubt yourself. Be willing to look forward from that point on without wondering what would have happened had you chosen something else.
- For example, if you need to turn in many assignments to pass a class, focus on how many you have to do and approach them one by one.
- Try to combine and solve problems together whenever possible. For example, if you're running out of time to study, try listening to a recorded lecture while walking to class or flip through note cards as you're waiting for dinner.
- For example, if you’re trying to pass a cumulative test, figure out what you already know and what you need to study for. Review everything you already know, then start learning more information from your notes, textbook, or other resources that may help you.
- Pay attention to know these scenarios make you feel.
- For example, if you have a deadline, you may skip cooking dinner or going to the gym so that you can give that time to your project.
- Cut down on unnecessary tasks whenever possible. For example, you might get your groceries delivered to you to save on shopping time. You can spend that time instead on other tasks.
Taking a Creative Approach
- If you’re making a complex decision, write down your alternatives. This way, you won’t forget any options and will be able to cross off any that aren’t plausible.
- For example, you might be hungry and need something to eat. Think about whether you want to cook food, get fast food, order takeout, or sit down at a restaurant.
- Problems like accepting the job across the country that offers good pay but takes you away from your family may require different ways of approach. Consider the logical solution, but also consider your thoughts, feelings, and the way the decision affects others.
- For example, if you’re buying a home and not sure how to make your final decision, talk to other homeowners about their thoughts or regrets about buying a home.
- For example, if you’re having financial difficulties, notice how your efforts are affecting the money coming in and the money you’re spending. If keeping a budget helps, keep with it. If using cash exclusively is a headache, try something else.
- Keep a journal where you record your progress, successes, and challenges. You can look at this for motivation when you are feeling discouraged.
Managing Your Emotions While Confronting Difficulties
- The first step is often the scariest. Try doing something small to start. For example, if you're trying to become more active, start going for daily walks.
- For example, if you’re overwhelmed by having a long to-do list, maybe the problems isn’t the list, but not saying “no” to things you can’t do.
- If you're feeling stressed, angry, or overwhelmed, you may be burned out. Make a list of things that cause stress or frustration. Try to cut down on these in the future. If you start feeling overwhelmed again, it may be a sign that you need to cut back.
- Find a therapist by calling your local mental health clinic or your insurance provider. You can also get a recommendation from a physician or friend.
Expert Q&A
- If you start feeling overwhelmed or frustrated, take a breather. Realize that every problem has a solution, but sometimes you're so wrapped up in it that you can't see anything but the problem. Thanks Helpful 3 Not Helpful 0
- Don't turn away from your problems. It will come back sooner or later and it will be more difficult to solve. Common sense can help to reduce the size of the problem. Thanks Helpful 1 Not Helpful 1
Tips from our Readers
- Just take it day by day and write down your plans to form a routine that works best for you. Even if you don't get everything done, just doing what you can for the day is enough.
- Turn the above steps into questions, then answer them. Make your goal actionable by detailing exactly how you'll attempt to achieve it.
- Talk to people you trust and who you believe can help. Be open and just tell them the truth about what's going on.
You Might Also Like
- ↑ https://hbr.org/2017/06/how-you-define-the-problem-determines-whether-you-solve-it
- ↑ https://www.cuesta.edu/student/resources/ssc/study_guides/critical_thinking/106_think_decisions.html
- ↑ https://au.reachout.com/articles/a-step-by-step-guide-to-problem-solving
- ↑ Rachel Clissold. Certified Life Coach. Expert Interview. 26 August 2020.
- ↑ https://serc.carleton.edu/geoethics/Decision-Making
- ↑ https://www.psychologytoday.com/blog/positive-psychology-in-the-classroom/201303/visualize-the-good-and-the-bad
- ↑ https://www.britannica.com/topic/operations-research/Resource-allocation
- ↑ https://www.niu.edu/citl/resources/guides/instructional-guide/brainstorming.shtml
- ↑ https://www.healthywa.wa.gov.au/Articles/N_R/Problem-solving
- ↑ https://www.collegetransfer.net/Home/ChangeSwitchTransfer/I-want-to/Earn-My-College-Degree/Overcoming-Obstacles
- ↑ https://psychcentral.com/lib/5-ways-to-solve-all-your-problems/
- ↑ https://www.apa.org/topics/psychotherapy/understanding
About This Article
To solve a problem, start by brainstorming and writing down any solutions you can think of. Then, go through your list of solutions and cross off any that aren't plausible. Once you know what realistic options you have, choose one of them that makes the most sense for your situation. If the solution is long or complex, try breaking it up into smaller, more manageable steps so you don't get overwhelmed. Then, focus on one step at a time until you've solved your problem. To learn how to manage your emotions when you're solving a particularly difficult problem, scroll down. Did this summary help you? Yes No
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5 steps (and 4 techniques) for effective problem solving.
Problem solving is the process of reviewing every element of an issue so you can get to a solution or fix it. Problem solving steps cover multiple aspects of a problem that you can bring together to find a solution. Whether that’s in a group collaboratively or independently, the process remains the same, but the approach and the steps can differ.
To find a problem solving approach that works for you, your team, or your company, you have to take into consideration the environment you’re in and the personalities around you.
Knowing the characters in the room will help you decide on the best approach to try and ultimately get to the best solution.
Table of Contents
5 problem solving steps, 4 techniques to encourage problem solving, the bottom line.
No matter what the problem is, to solve it, you nearly always have to follow these problem solving steps. Missing any of these steps can cause the problem to either resurface or the solution to not be implemented correctly.
Once you know these steps, you can then get creative with the approach you take to find the solutions you need.
1. Define the Problem
You must define and understand the problem before you start, whether you’re solving it independently or as a group. If you don’t have a single view of what the problem is, you could be fixing something that doesn’t need fixing, or you’ll fix the wrong problem.
Spend time elaborating on the problem, write it down, and discuss everything, so you’re clear on why the problem is occurring and who it is impacting.
Once you have clarity on the problem, you then need to start thinking about every possible solution . This is where you go big and broad, as you want to come up with as many alternative solutions as possible. Don’t just take the first idea; build out as many as you can through active listening, as the more you create, the more likely you’ll find a solution that has the best impact on the team.
3. Decide on a Solution
Whichever solution you pick individually or as a team, make sure you think about the impact on others if you implement this solution. Ask questions like:
- How will they react to this change?
- Will they need to change anything?
- Who do we need to inform of this change?
4. Implement the Solution
At this stage of problem solving, be prepared for feedback, and plan for this. When you roll out the solution, request feedback on the success of the change made.
5. Review, Iterate, and Improve
Making a change shouldn’t be a one time action. Spend time reviewing the results of the change to make sure it’s made the required impact and met the desired outcomes.
Make changes where needed so you can further improve the solution implemented.
Each individual or team is going to have different needs and may need a different technique to encourage each of the problem solving steps. Try one of these to stimulate the process.
1-2-4 All Approach + Voting
The 1-2-4-All is a good problem solving approach that can work no matter how large the group is. Everyone is involved, and you can generate a vast amount of ideas quickly.
Ideas and solutions are discussed and organized rapidly, and what is great about this approach is the attendees own their ideas, so when it comes to implementing the solutions, you don’t have more work to gain buy-in.
As a facilitator, you first need to present the group with a question explaining the problem or situation. For example, “What actions or ideas would you recommend to solve the company’s lack of quiet working areas?”
With the question clear for all to see, the group then spends 5 minutes to reflect on the question individually. They can jot down their thoughts and ideas on Post-Its.
Now ask the participants to find one or two other people to discuss their ideas and thoughts with. Ask the group to move around to find a partner so they can mix with new people.
Ask the pairs to spend 5 minutes discussing their shared ideas and thoughts.
Next, put the group into groups of two or three pairs to make groups of 4-6. Each group shouldn’t be larger than six as the chances of everyone being able to speak reduces.
Ask the group to discuss one interesting idea they’ve heard in previous rounds, and each group member shares one each.
The group then needs to pick their preferred solution to the problem. This doesn’t have to be voted on, just one that resonated most with the group.
Then ask for three actions that could be taken to implement this change.
Bring everyone back together as a group and ask open questions like “What is the one thing you discussed that stood out for you?” or “Is there something you now see differently following these discussions?”
By the end of the session, you’ll have multiple approaches to solve the problem, and the whole group will have contributed to the future solutions and improvements.
The Lightning Decision Jam
The Lightning Decision Jam is a great way to solve problems collaboratively and agree on one solution or experiment you want to try straight away. It encourages team decision making, but at the same time, the individual can get their ideas and feedback across. [1]
If, as a team, you have a particular area you want to improve upon, like the office environment, for example, this approach is perfect to incorporate in the problem solving steps.
The approach follows a simple loop.
Make a Note – Stick It on The Wall – Vote – Prioritize
Using sticky notes, the technique identifies major problems, encourages solutions, and opens the group up for discussion. It allows each team member to play an active role in identifying both problems and ways to solve them.
Mind Mapping
Mind mapping is a fantastic visual thinking tool that allows you to bring problems to life by building out the connections and visualizing the relationships that make up the problem.
You can use a mind map to quickly expand upon the problem and give yourself the full picture of the causes of the problem, as well as solutions [2] .
The goal of a mind map is to simplify the problem and link the causes and solutions to the problem.
To create a mind map, you must first create the central topic (level 1). In this case, that’s the problem.
Next, create the linked topics (level 2) that you place around and connect to the main central topic with a simple line.
If the central topic is “The client is always changing their mind at the last minute,” then you could have linked topics like:
- How often does this happen?
- Why are they doing this?
- What are they asking for?
- How do they ask for it?
- What impact does this have?
Adding these linking topics allows you to start building out the main causes of the problem as you can begin to see the full picture of what you need to fix. Once you’re happy that you’ve covered the breadth of the problem and its issues, you can start to ideate on how you’re going to fix it with the problem solving steps.
Now, start adding subtopics (level 3) linking to each of the level 2 topics. This is where you can start to go big on solutions and ideas to help fix the problem.
For each of the linked topics (level 2), start to think about how you can prevent them, mitigate them, or improve them. As this is just ideas on paper, write down anything that comes to mind, even if you think the client will never agree to it!
The more you write down, the more ideas you’ll have until you find one or two that could solve the main problem.
Once you run out of ideas, take a step back and highlight your favorite solutions to take forward and implement.
The 5 Why’s
The five why’s can sound a little controversial, and you shouldn’t try this without prepping the team beforehand.
Asking “why” is a great way to go deep into the root of the problem to make the individual or team really think about the cause. When a problem arises, we often have preconceived ideas about why this problem has occurred, which is usually based on our experiences or beliefs.
Start with describing the problem, and then the facilitator can ask “Why?” fives time or more until you get to the root of the problem. It’s tough at first to keep being asked why, but it’s also satisfying when you get to the root of the problem [3] .
As a facilitator, although the basic approach is to ask why, you need to be careful not to guide the participant down a single route.
To help with this, you can use a mind map with the problem at the center. Then ask a why question that will result in multiple secondary topics around the central problem. Having this visual representation of the problem helps you build out more useful why questions around it.
Once you get to the root of the problem, don’t forget to be clear in the actions to put a fix in place to resolve it.
Learn more about how to use the five why’s here .
To fix a problem, you must first be in a position where you fully understand it. There are many ways to misinterpret a problem, and the best way to understand them is through conversation with the team or individuals who are experiencing it.
Once you’re aligned, you can then begin to work on the solutions that will have the greatest impact through effective problem solving steps.
For the more significant or difficult problems to solve, it’s often advisable to break the solution up into smaller actions or improvements.
Trial these improvements in short iterations, and then continue the conversations to review and improve the solution. Implementing all of these steps will help you root out the problems and find useful solutions each time.
| [1] | ^ | UX Planet: |
| [2] | ^ | Focus: |
| [3] | ^ | Expert Program Management: |
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6 Creative Ways to Solve a Problem
Creative problem-solving strategies separate forward-moving solutions from quick fixes. Truly an art, creative strategies address challenges by guiding you to see challenges in a whole new light. Can crisis equal opportunity? With these 6 creative ways to solve a problem, the answer is often a resounding yes.
1. Six Step Problem-Solving Model
Some problems seem overwhelming in their complexity. You don’t know where to begin. And this lack of direction can leave you running in circles.
The six step problem-solving model aids you by creating a structured, coherent approach to problem solving. In a sense, it gives you the opportunity to step back, take a breath, and approach the issue methodically.
The six steps of this method are:
- Define the problem.
- Define the root cause or causes of the problem.
- Develop possible solutions.
- Choose the best-seeming solution from the list.
- Implement the solution.
- Evaluate the outcome of the solution.
Although the steps are sequential, any one of them can be repeated. For instance, deep thought about Step 4 might lead you to realize that you defined the root causes of the problem in step 2 incorrectly. And evaluation of outcomes at the final stage may be negative, calling upon you to repeat the process. In this sense, the model functions as a sort of algorithm, with feedback loops at each stage.
2. Drill-Down Technique
Defining root causes of a problem is often the most difficult part of problem solving. You know that something is wrong. You see something isn’t working. But the causes remain vague or elusive. The drill-down technique helps you resolve this issue by breaking the problem down into progressively smaller pieces. More accurately, you define a large problem and “drill down” closer and closer to the root causes.
To use the drill-down technique, you will draw a simple table. On the left side you write down the problem you face. To the right, in the middle, you list possible causes of that problem. And even further to the right, you will list potential causes of each of the middle issues. Although it sounds complicated, a graphic example shows how easy it is:
Sales are Down | Store Inventory is Low | Supplier is Unreliable |
| Some Items Discontinued | ||
Outside Sales Team Below Goals | High Team Turnover | |
| Low Team Morale |
In this simple example, you’ve drilled down from one large problem to its core issues. Once you know root causes, solutions present themselves more easily. In this case, you may consider looking at a new, more reliable supplier that has items similar to ones that have been discontinued. At the same time, you may want to meet with the outside sales team to show you care about their challenges and help to address them.
3. Reverse Brainstorming
You likely have some familiarity with brainstorming techniques . That is, a gathering of interested parties to throw out spontaneous solutions to a problem without judgment. Often, a team leader facilitates the brainstorming session by writing the team’s ideas on a white board. With practice, you can brainstorm on your own, too.
But what is reverse brainstorming?
The process may appear the same to an outsider. The difference lies in the fact that you don’t try to find solutions to the problem. You’re looking for ways to make the problem worse
With reverse brainstorming, everyone offers how to decrease sales, increase employee turnover, raise expenses—bring us your worst. It may seem silly at first, but people will get quite focused and creative as the brainstorming period evolves. Once you have a satisfactory number of negative solutions, work on reversing them to uncover the real solutions. The method is highly effective at finding new angles to solve problems.
4. Reverse Engineer—Work Backwards Problem Solving Strategy
While we’re in reverse, let’s look at the “work backwards problem solving strategy.” With origins in mathematics and engineering, it’s not for everyone. But you hardly need a mathematics degree to try it out. It requires mostly patience with yourself as you learn to “walk backward.”
We usually approach problems from a starting point of the present. Then, we define the consecutive steps required to reach our goal. But any particular step may lead us off the best, most efficient path. But sometimes, plans in action go completely astray when implemented. Backwards problem solving serves as a sort of check against this possibility.
With the work backwards strategy to problem solving, you start with your goal . Then you work backward: what was the final stage prior to reaching that goal? And what came before that? Step by step, you work backward to the situation as it currently exists. When you are finished, compare the stages to your more standard, forward plan. Where are they the same, and how do they differ?
5. Make the Problem Bigger (aka 10X Problem Solving or the Eisenhower Principle
The 10X Rule teaches you to reach for 10X the success. What if you attempted to solve problems by making them—or at least, imagining them to be—10X bigger?
Any organization faces a multitude of problems. Managers or entrepreneurs race to resolve one mini “crisis” after another. In this rushed state, it’s easy to lose perspective of the issues that are truly critical. But not all problems deserve the same amount of attention. One way to manage task prioritization is to imagine that each issue is 10 times bigger.
Suppose you manage an office staff of 10. Three issues arise. An employee is consistently 10 minutes late, a company computer has gone missing, and your administrative assistant neglected to schedule your important lunch meeting. Each issue needs to be resolved. And at an emotional level, the late employee gets under your skin in particular.
But imagine the problems as 10 times bigger, and you may prioritize differently. One missing computer seems easy to put off. But the entire office would grind to a standstill if 10 of them were missing. Your first move may be to call security to help resolve the issue, then address your administrative assistant’s lack of focus. After all, 10 missed lunch meetings could be disastrous when one of them is with the CEO. The tardy employee can wait until the end of the day.
This process, famously used by General Eisenhower on the battlefield, allows you to take a step back and see issues more holistically. You develop a big picture to assist you in prioritization.
6. Don’t Just Step Back—Sleep on It
Each of the above creative problem-solving strategies uses an entirely different method. And yet, they all share one thing in common: they help you step back and re-assess the problem in a new way. But if you find yourself embroiled in a single, complex problem—the sort of thing that consumes your days and weeks—you may need to do more than simply step back. You might want to sleep on it.
We sometimes over-emphasize the benefits of “sticking with it.” We admire the person who works hard, stays up late, and gets up early to attack the problem again. But lack of sleep not only takes a toll on your health. It can also prevent your brain from doing what it is designed to do during rest. That is, process and correlate the information of the day in ways our waking minds may have missed.
Abundant research makes clear that a proper night’s sleep aids in problem solving . That time you woke up refreshed and a solution seemed clear? That wasn’t a unique occurrence. The process has been widely documented across cultures. Historically, Thomas Edison, Albert Einstein, and others have resolved complex problems during sleep.
Yes, you might sometimes need to burn the midnight oil to catch up on routine tasks. Filing taxes, meeting payroll, and ordering inventory are valid reasons to miss a little sleep if they all hit at once. But for complex problem solving—and overall health and wellness—don’t deprive yourself of sleep for long periods. That night of quality sleep might provide unique, creative solutions your overworked conscious mind would have never imagined.
Photo by mavo/Shutterstock
Bryan Lindenberger
Bryan enjoys the digital space where arts and technology meet. As a writer, he has worked in education, health and wellbeing, and manufacturing. He also assists smaller businesses in web development including accessibility and content development. In his free time, he hikes trails in central Florida.
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Stumped five ways to hone your problem-solving skills.
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Respect the worth of other people's insights
Problems continuously arise in organizational life, making problem-solving an essential skill for leaders. Leaders who are good at tackling conundrums are likely to be more effective at overcoming obstacles and guiding their teams to achieve their goals. So, what’s the secret to better problem-solving skills?
1. Understand the root cause of the problem
“Too often, people fail because they haven’t correctly defined what the problem is,” says David Ross, an international strategist, founder of consultancy Phoenix Strategic Management and author of Confronting the Storm: Regenerating Leadership and Hope in the Age of Uncertainty .
Ross explains that as teams grapple with “wicked” problems – those where there can be several root causes for why a problem exists – there can often be disagreement on the initial assumptions made. As a result, their chances of successfully solving the problem are low.
“Before commencing the process of solving the problem, it is worthwhile identifying who your key stakeholders are and talking to them about the issue,” Ross recommends. “Who could be affected by the issue? What is the problem – and why? How are people affected?”
He argues that if leaders treat people with dignity, respecting the worth of their insights, they are more likely to successfully solve problems.
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Best 5% interest savings accounts of 2024, 2. unfocus the mind.
“To solve problems, we need to commit to making time to face a problem in its full complexity, which also requires that we take back control of our thinking,” says Chris Griffiths, an expert on creativity and innovative thinking skills, founder and CEO of software provider OpenGenius, and co-author of The Focus Fix: Finding Clarity, Creativity and Resilience in an Overwhelming World .
To do this, it’s necessary to harness the power of the unfocused mind, according to Griffiths. “It might sound oxymoronic, but just like our devices, our brain needs time to recharge,” he says. “ A plethora of research has shown that daydreaming allows us to make creative connections and see abstract solutions that are not obvious when we’re engaged in direct work.”
To make use of the unfocused mind in problem solving, you must begin by getting to know the problem from all angles. “At this stage, don’t worry about actually solving the problem,” says Griffiths. “You’re simply giving your subconscious mind the information it needs to get creative with when you zone out. From here, pick a monotonous or rhythmic activity that will help you to activate the daydreaming state – that might be a walk, some doodling, or even some chores.”
Do this regularly, argues Griffiths, and you’ll soon find that flashes of inspiration and novel solutions naturally present themselves while you’re ostensibly thinking of other things. He says: “By allowing you to access the fullest creative potential of your own brain, daydreaming acts as a skeleton key for a wide range of problems.”
3. Be comfortable making judgment calls
“Admitting to not knowing the future takes courage,” says Professor Stephen Wyatt, founder and lead consultant at consultancy Corporate Rebirth and author of Antidote to the Crisis of Leadership: Opportunity in Complexity . “Leaders are worried our teams won’t respect us and our boards will lose faith in us, but what doesn’t work is drawing up plans and forecasts and holding yourself or others rigidly to them.”
Wyatt advises leaders to heighten their situational awareness – to look broadly, integrate more perspectives and be able to connect the dots. “We need to be comfortable in making judgment calls as the future is unknown,” he says. “There is no data on it. But equally, very few initiatives cannot be adjusted, refined or reviewed while in motion.”
Leaders need to stay vigilant, according to Wyatt, create the capacity of the enterprise to adapt and maintain the support of stakeholders. “The concept of the infallible leader needs to be updated,” he concludes.
4. Be prepared to fail and learn
“Organisations, and arguably society more widely, are obsessed with problems and the notion of problems,” says Steve Hearsum, founder of organizational change consultancy Edge + Stretch and author of No Silver Bullet: Bursting the Bubble of the Organisational Quick Fix .
Hearsum argues that this tendency is complicated by the myth of fixability, namely the idea that all problems, however complex, have a solution. “Our need for certainty, to minimize and dampen the anxiety of ‘not knowing,’ leads us to oversimplify and ignore or filter out anything that challenges the idea that there is a solution,” he says.
Leaders need to shift their mindset to cultivate their comfort with not knowing and couple that with being OK with being wrong, sometimes, notes Hearsum. He adds: “That means developing reflexivity to understand your own beliefs and judgments, and what influences these, asking questions and experimenting.”
5. Unleash the power of empathy
Leaders must be able to communicate problems in order to find solutions to them. But they should avoid bombarding their teams with complex, technical details since these can overwhelm their people’s cognitive load, says Dr Jessica Barker MBE , author of Hacked: The Secrets Behind Cyber Attacks .
Instead, she recommends that leaders frame their messages in ways that cut through jargon and ensure that their advice is relevant, accessible and actionable. “An essential leadership skill for this is empathy,” Barker explains. “When you’re trying to build a positive culture, it is crucial to understand why people are not practicing the behaviors you want rather than trying to force that behavioral change with fear, uncertainty and doubt.”
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How to Handle a Problem You Can’t Solve
Finding a solution is only one way to proactively respond to problems..
Posted July 22, 2021 | Reviewed by Vanessa Lancaster
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- The difference between a big problem and a small problem is the amount of risk we’re exposed to.
- New research has uncovered an often overlooked category of solutions to help solve difficult problems.
- Sometimes it's more productive to eliminate, shrink, or delegate a problem than it is to solve it.
After returning from a 12-month deployment in Iraq, Patrick Skluzacek began to experience horrible nightmares. Veterans Affairs didn’t have a cure. Afraid to close his eyes, Patrick turned to alcohol to help himself sleep. As his drinking and mental health grew worse, he went on to lose his job, his wife, and even his home.
Patrick’s son Tyler was desperate to help. But he wasn’t a psychologist or a sleep expert. He was just a college student studying mathematics and computer science. So rather than trying to heal his father from the effects of trauma, Tyler decided to look for a way to prevent the nightmares from happening.
Using his programming skills, Tyler developed a smartwatch app that monitored his father’s heart rate and movement during sleep to spot nightmares early. The app then prompted the watch to vibrate gently, coaxing Patrick out of bad dreams without completely waking him.
With the help of his son’s invention, Patrick has once again lived a normal life.
Thankfully, most of us have never had to watch a parent struggle with post- traumatic stress disorder, but we’ve all faced problems that felt too big to solve–in our professional lives as well as at home. The experience of the Skluzaceks, both father and son, illustrates some strategies you might employ the next time you’re up against what feels like an impossible dilemma.
1. If you can’t solve a problem, look for ways to eliminate it.
Problems live inside systems, and one way to get rid of a problem is to eliminate the system it belongs to. Tyler never found a cure for his dad’s PTSD . He simply found a way to interrupt his father’s nightmares, preventing them from happening again.
In an organizational context, we can usually wipe out problems that seem unsolvable by replacing troublesome staff, software, or policies. But new research out of the University of Virginia has found that our brains often overlook these “subtractive solutions”— tunneling instead on what might be added to improve a situation.
2. If you can’t eliminate a problem, look for ways to shrink it.
The difference between a big problem and a small problem is the amount of risk we’re exposed to. So if you can’t fix the cause, try to reduce the effects. For example, certain positions in your company might be inherently stressful , posing the threat of high burnout rates. If you can’t find a way to modify the positions to make them less demanding, an alternative might be to offer more vacation days or free massage therapy sessions to the affected individuals. The root problem will still exist, but it will have a smaller negative impact on your organization.
3. See if you can delegate the problem to someone else.
As Tyler’s story illustrates, sometimes we are our own best options. But in many cases, we can turn to others for help. A surprising number of leaders are comfortable delegating tasks but never think to delegate problems. Doing so can free up your time and empower your colleagues to make a bigger impact. Plus, most problems are easier to solve with a fresh perspective, making a handoff even more advantageous.
4. Ask yourself what insight would make the problem easier to solve.
If you can’t solve a problem, it might be indicative of a gap in your expertise. That’s perfectly normal. The key is simply to pinpoint what those gaps are. To do so, try filling in this sentence:
I would be able to solve this problem if only I knew…
Once you’ve identified the gaps in your knowledge, brainstorm ways to find reliable answers, colleagues might be a useful resource, and consulting is often an effective option. If your timeline and budget don’t allow for consulting, on-demand online trainings are another way to expand your understanding, and a surprising number of experts offer these virtual courses.
5. Question whether you actually need to solve the problem right now.
Sometimes, the true cost of a problem is the work it distracts you from. In Tyler’s case, ignoring his father’s nightmares wasn’t an option. But sometimes, procrastinating on one problem allows you to be more productive in other areas. If you’re facing a dilemma that seems unsolvable, try asking yourself if fixing it is really your best opportunity for personal growth or organizational contribution at that moment. Will you incur any high costs by waiting to tackle the issue?
Challenges don’t always have an obvious cure, but you can still respond intentionally and productively. In fact, knowing what to do with tough dilemmas is a skill that sets great leaders apart. After all, difficult decisions are one of the primary responsibilities great leaders get paid to handle.
Kyle Young is a strategy consultant and writer who works to help people achieve their goals.
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Sticking up for yourself is no easy task. But there are concrete skills you can use to hone your assertiveness and advocate for yourself.
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1. Calm your emotions. Making a decision or solving a problem can be difficult if you feel anxious or nervous about how it will go. If your fear is clouding your ability to solve a problem, take a moment to feel calm. Take a few slow, deep breaths to help calm your nervous system and com back into the present moment.
4. Implement the Solution. At this stage of problem solving, be prepared for feedback, and plan for this. When you roll out the solution, request feedback on the success of the change made. 5. Review, Iterate, and Improve. Making a change shouldn't be a one time action.
Although problem-solving is a skill in its own right, a subset of seven skills can help make the process of problem-solving easier. These include analysis, communication, emotional intelligence, resilience, creativity, adaptability, and teamwork. 1. Analysis. As a manager, you'll solve each problem by assessing the situation first.
You can set project goals (e.g. do this task and then this task, etc.) or time goals (work on this task for 4 hours). Taking manageable steps is important, because trying to tackle the problem all ...
Here are the seven steps of the rational approach: Define the problem. Identify possible causes. Brainstorm options to solve the problem. Select an option. Create an implementation plan. Execute the plan and monitor the results. Evaluate the solution. Read more: Effective Problem Solving Steps in the Workplace.
The four-step process consists of asking a series of questions and using the answers to create a problem statement that will elicit novel ideas from an array of experts. Establish the need for a ...
Here are three tips for executing step one like an expert. 1. Organize knowledge correctly. Often, novices have all the knowledge they need to solve the problem at hand. They just can't get to ...
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In a sense, it gives you the opportunity to step back, take a breath, and approach the issue methodically. The six steps of this method are: Define the problem. Define the root cause or causes of ...
Problem-solving strategies can be helpful in many situations. Thinking creatively and testing out different potential solutions can help you come up with alternative ways of solving your problems.
To make use of the unfocused mind in problem solving, you must begin by getting to know the problem from all angles. "At this stage, don't worry about actually solving the problem," says ...
Doing so can free up your time and empower your colleagues to make a bigger impact. Plus, most problems are easier to solve with a fresh perspective, making a handoff even more advantageous. 4 ...
In this episode, Frei explains how you can solve any problem in five clear steps. First, she says, start by identifying the real problem holding you back. Then move on to building trust and ...
Similarly to this head-scratching school bus logic puzzle, the math problem "6 + 4 = 4" has a trick to it. Each of the numbers in this equation is built from matchsticks. By moving only one ...
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First, don't just rely on the data. Take facts, especially observable ones, into account. Second, consider how you're framing the problem statement. It should present the problem in a way that ...
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The key customer service problem-solving techniques. Now that you've gone over all the common customer complaints and queries, it's time to focus on making sure they don't happen again. To help with that, here are the top customer service problem-solving best practices guaranteed to delight customers. Empathy, active listening, and ...
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