Question

How do you solve `abs(-4+5x)=16`?

Answer 1

`x=-12/5,4`

Explanation:

Solve:

`abs(-4+5x)=16`

Since `absa=+a and -a`, the equation can be broken into positive and a negative equations.

`-4+5x=16`

and

`-(-4+5x)=16`

Positive Equation

`-4+5x=16`

Add `4` to both sides.

`-color(red)cancel(color(black)(4))+color(red)cancel(color(black)(4))+5x=16+4`

Simplify.

`5x=20`

Divide both sides by `5`.

`(color(red)cancel(color(black)(5))x)/color(red)cancel(color(black)(5))=20/5`

Simplify.

`x=4`

Negative Equation

`-(-4+5x)=16`

Distribute the `-1` on the left-hand side.

`4-5x=16`

Subtract `4` from both sides.

`color(red)cancel(color(black)(4))-color(red)cancel(color(black)(4))-5x=16-4`

Simplify.

`-5x=12`

Divide both sides by `-5`.

`(color(red)cancel(color(black)(-5))x)/(color(red)cancel(color(black)(-5))x)=12/(-5)`

`x=-12/5`

Collect all solutions.

`x=-12/5,4`