Often the absolute value will have more than just a variable in it. In this case we will have to solve the resulting equations when we consider the positive and negative possibilities. This is shown in the next example. Example `|2x − 1| = 7`

`|2x − 1| = 7`	Absolute value can be positive or negative
`2x−1=7 or 2x−1=−7`	Two equations to solve

Now notice we have two equations to solve, each equation will give us a different solution. Both equations solve like any other two-step equation.

`2x−1=7`	`2x−1=-7`
`2x−1color(red)(+1)=7color(red)(+1)`	`2x−1color(red)(+1)=-7color(red)(+1)`
`2x=8`	`2x=-6`
`(2x)/color(red)(2)=8/color(red)(2) `	`(2x)/color(red)(2)=(-6)/color(red)(2) `
`x=4 `	`x= -3`

Example `2−4|2x+3|=−18`

`2−4|2x+3|=−18 `	Notice absolute value is not alone
`2color(red)(-2)−4|2x+3|=−18color(red)(-2) `	Subtract `2` from both sides
`−4|2x+3|=−20`	Absolute value still not alone
`(−4|2x+3|)/color(red)(-4)=(−20)/color(red)(-4)`	Divide both sides by `−4`
`|2x+3|=5`	Absolute value can be positive or negative
`2x+3=5` or `2x+3=−5`	Two equations to solve

`2x+3=5`	`2x+3=−5`
`2x+3color(red)(-3)=5color(red)(-3)`	`2x+3color(red)(-3)=-5color(red)(-3)`
`2x=2`	`2x=-8`
`(2x)/color(red)(2)=2/color(red)(2)`	`(2x)/color(red)(2)=(-8)/color(red)(2)`
`x=1`	`x=−4`