How to Solve a Linear Equation with One Variable

In most upper level mathematics courses, you will, at one point or another, be asked to solve a linear equation. In fact, solving linear equations is often the first step to other problems, like graphing lines, and is the basis for many word problems in math. Linear equations can be scary at first, but if you have the right math skills and are taught some nice tricks, solving them can be easier than you think. There are many different ways to solve linear equations, this is just the way I do it.

When solving linear equations with one variable, you want the variable by itself. The first step in getting the variable by itself is to move all the constants to one side. I tend to try to keep my variable on the left, so I will always move my constants to the right side of the equation. To move a constant, you have to do the opposite operation. When a constant is being added, you will have to subtract it, and vice versa.

5x+10=25

To move the constant, 10, to the opposite of the variable, you have to subtract 10 from both sides, because the opposite of addition is subtraction.

5x+10-10=25-10
5x=15

This leaves our 5x by itself. Unfortunately, that x still isn't alone, so we have to get rid of the 5. Again, you have to do the opposite operation to move the 5 to the other side of the equation. Because the 5 is being multiplied, we will have to divide it.

5x/5=15/5
x=3

According to our answer, our variable, x, is equal to 3!

It is always a good idea to check that your answer is right. To check your answer, you will want to replace the variable you began with, with the number you got as your final answer.

5x+10=25
5(3)+10=25
15+10=25
25=25

It looks like our answer is right! With that, I will leave you to your own equations. Good luck and happy solving!