When solving equations with absolute value we can end up with more than one possible answer. This is because what is in the absolute value can be either negative or positive and we must account for both possibilities when solving equations. This is illustrated in the following example. Example

`|x|= 7`	Absolute value can be positive or negative
`x=7` or `x=−7`	Solution

Notice that we have considered two possibilities, both the positive and negative. Either way, the absolute value of our number will be positive 7. Example

`−4|x|=−20`	Notice absolute value is not alone
`(−4|x|)/color(red)(-4)=(−20)/color(red)(-4)`	Divide both sides by `−4`
`|x|=5`	Absolute value can be positive or negative
`x=5 or x=−5`	Solution

Example `5+|x|=8`

`5+|x|=8`	Notice absolute value is not alone
`5+|x|color(red)(-5)=8color(red)(-5)`	Subtract 5 from both sides
`|x|=3 `	Absolute value can be positive or negative
`x=3 or x=−3`	solution

Example

`5|x|−4=26`	Notice the absolute value is not alone
`5|x|−4color(red)(+4)=26color(red)(+4)`	Add `4` to both sides
`5|x| = 30`	Absolute value still not alone
`(5|x|)/color(red)(5) = (30)/color(red)(5)`	Divide both sides by `5`
`|x|=6`	Absolute value can be positive or negative
`x=6 or x=−6`	Solution