Question

How do you solve `abs [x]= 2x +6`?

Answer 1

`x=-2`

Explanation:

We can split up the absolute value into two functions
`x=2x+6`
`-x=2x+6`

Solving for `x` in the first equation we get the following
`-x=6`
`x=-6`

Solving for the second equation we get the following
`-3x=6`
`x=-2`

We need to plug the values into the function to make sure all the answers we got satisfy the conditions.
`x=-6`
`\abs{-6}=2(-6)+6`
`6=-12+6`
`6\ne -6`
So we know `x=-6` is not a solution.

`x=-2`
`\abs{-2}=2(-2)+6`
`2=-4+6`
`2=2`
So `x=-2` is a solution.