Solving Two-Step Linear Equations
As we solve two-step equations, the important thing to
remember is that we do the opposite to both sides of the
equation. With each step, we get closer to getting the variable
by itself, basically working backwards. This means we will add
or subtract first, then multiply or divide second.
Example 1:
4x – 20 = - 8
+ 20 = +20
4x
4
x
= 12
4
= 3
Add 20 to both sides
Divide both sides by 4
To check our answer: 4(3) – 20 = - 8
12 – 20 = - 8
- 8=-8
Example 2:
5x + 7 = 7
-7 -7
5x
=0
5
5
x
=0
Subtract 7 from both sides
Divide both sides by 5
Modified from Beginning and Intermediate Algebra, by Tyler Wallace, CC-BY 2010. Licensed under a
Creative Commons Attribution 3.0 Unported License (http://creativecommons.org/licenses/by/3.0)
A common error students make with two-step equations is with
negative signs. The sign always stays with the number,
sometimes resulting in a negative number.
Example 3:
Example 4:
4 – 2x = 10
-4
-4
- 2x = 6
-2 -2
x=-3
8–x= 2
-8
-8
-x=-6
- 1x = - 6
-1 -1
x= 6
Subtract 4 from both sides
Divide both sides by -2
Subtract 8 from both sides
No number in front of the variable means 1
Divide both sides by -1
Modified from Beginning and Intermediate Algebra, by Tyler Wallace, CC-BY 2010. Licensed under a
Creative Commons Attribution 3.0 Unported License (http://creativecommons.org/licenses/by/3.0)