After mastering the technique for solving equations that are simple one-step equations, we are ready to consider two-step equations. As we solve two-step equations, the important thing to remember is that everything works backwards! When solving for our variable x, we use order of operations backwards as well. This means we will add or subtract first, then multiply or divide second (then exponents, and finally any parentheses or grouping symbols, but that’s another lesson). So to solve the equation We have two numbers on the same side as the `x`. We need to move the `4` and the `20` to the other side. We know to move the four we need to divide, and to move the twenty we will add twenty to both sides. If order of operations is done backwards, we will add or subtract first. Therefore we will add `20` to both sides first. Once we are done with that, we will divide both sides by `4`. The steps are shown below.

`4x−20=−8 `	Start by focusing on the subtract 20
`4x−20color(red)(-20)=−8 color(red)(-20)`	Add `20` to both sides
`4x =12 `	Now we focus on the `4` multiplied by `x`
`(4x)/color(red)(4) =12/color(red)(4) `	Divide both sides by `4`
`x=3 `	Solution!

The same process is used to solve any two-step equations. Add or subtract first, then multiply or divide. Consider our next example and notice how the same pro- cess is applied. Example

`5x+7= 7`	Start by focusing on the plus `7`
`5x+7color(red)(-7)= 7color(red)(-7)`	Subtract `7` from both sides
`5x=0 `	Now focus on the multiplication by `5`
`(5x)/color(red)(5)=0/color(red)(5) `	Divide both sides by 5
`x=0 `	Solution!

Notice the seven subtracted out completely! Many students get stuck on this point, do not forget that we have a number for “nothing left” and that number is zero. A common error students make with two-step equations is with negative signs. Remember the sign always stays with the number. Consider the following example. Example ``

`4−2x=10`	Start by focusing on the positive 4
`4color(red)(-4)−2x=10color(red)(-4)`	Subtract `4` from both sides
`−2x=6`	Negative (subtraction) stays on the `2x`
`(−2x)/color(red)(-2)=6/color(red)(-2)`	Divideby−2
`x=-3`	Solution!

The same is true even if there is no coefficient in front of the variable. Consider the next example. Example

`8 − x = 2 `	Start by focusing on the positive `8`
`8color(red)(-8) − x = 2color(red)(-8) `	Subtract `8` from both sides
`− x = − 6 `	Negative (subtraction) stays on the `x`
`− 1x = − 6`	Remember, no number in front of variable means `1`
`(−1x)/color(red)(-1) = (−6)/color(red)(-1)`	Divide both sides by `−1`
`x=6`	Solution!

More Examples: