How To Solve Equations (Part 1)

How should you think about equations? And how can you solve them? Keep on reading to find out!

Jason Marshall, PhD
4-minute read
Episode #153

How To Solve Equations (Part 1)

In the last episode of Math Dude, we learned that an equation is a proclamation that the expression on one side of an equals sign has the exact same value as the expression on the other. But what exactly does that mean? And how do you use equations to solve problems and do useful things? Stay tuned because those are precisely the questions we’ll be answering today and over the next few weeks..

How to Solve an Equation

When you plug in just the right number for the variable, the expressions on either side of the equals sign in the equation


must have the exact same value. After all, that’s what an equation means! But how do you find that special value—the “solution” to the equation? As we’ll see over the next few weeks, there are actually several different ways to do it. The method we’re going to talk about today is by no means the best for most situations, but it’s nonetheless a helpful one to keep in the back of your mind. This method is the most rudimentary of all methods—we’re talking about good old brute force.

What does that mean in terms of math? It means that we start by guessing that the value of the variable must be equal to 1, and we then calculate the values that the left and right expressions will have. If the two expressions are equal, we’re done. If not, we move on to the next guess and calculate the values of the two sides when the variable is equal to 2. We then check again and we repeat as necessary until we find the value of the variable that gives us a match.

Here are the values of the expressions on the left and right side of our equation for guesses ranging from 1 to 5:


For guesses of 1, 2, and 3, the value of the left expression is greater than the value of the right. For a guess of 5, the value of the left expression is less than the value of the right. And, lo and behold, the left and right expressions have the exact same value for a guess of 4. Which means that this equation is solved by setting the variable to 4.


About the Author

Jason Marshall, PhD

Jason Marshall is the author of The Math Dude's Quick and Dirty Guide to Algebra. He provides clear explanations of math terms and principles, and his simple tricks for solving basic algebra problems will have even the most math-phobic person looking forward to working out whatever math problem comes their way.