The Flow for Solving Linear Equations

Let's talk about solving linear or one-variable equations. The one-variable equation is the most basic type of equation, which you'll see in an algebra course. You definitely want to make sure you master it. When you are solving a one-variable equation, there are four general steps. You can consider it more like a flow because sometimes you don't have to use all the steps.

Consider the goal. Your goal is to get the variable by itself. First, check if you need to simplify both sides or not. At this point, you'll simplify each side of the equal sign like an expression. Step 2 and 3 are properties of equality. With steps 2 and 3, think of a balance or a pair of scales - whatever you do one side, you have to do to the other. Whatever you want to undo, you do the opposite in order to cancel it out. With addition, you do subtraction and vice versa. When multiplying, you either divide or multiply both sides by the reciprocal.

Here are some examples:

Solving equations can be both an art and science. With equations, you can always verify your answers, so I would definitely check your answers.

Another tip for solving equations. Since you can use the properties of equality at any time, you can multiply both sides by the LCD to remove the fractions. When you do this, make sure you distribute to each term.

For more on simplifying expressions, check out my youtube channel. If you have any questions or blog ideas, you can e-mail me at jdmathguy@gmail.com

-JD