Question

How do you solve `abs(5x + 10) - 15 = 20`?

Answer 1

`x=-9,5`

Explanation:

Rearrange the equation:
`|5x+10|-15=20`

=>

`|5x+10|=35`

Because of the modulus there are two solutions, the first:

`5x+10=35` => `x=5`

The second:

`5x+10=-35` => `x=-9`

Answer 2

`x=-9, 5`

Explanation:

`abs(5x+10)-15=20`

Add `15` to both sides of the equation.

`abs(5x+10)=20+15` =

`abs(5x+10)=35`

Rewrite the equation without the absolute value symbol, with one equation positive, and one negative.

`5x+10=35` and

`-(5x+10)=35`.

Positive Equation

`5x+10=35`

Subtract `10` from both sides of the equation.

`5x=35-10` =

`5x=25`

Divide both sides by `5`.

`x=25/5` =

`x=5`

Negative Equation

`-(5x+10)=35` =

`-5x-10=35`

Add `10` to both sides.

`-5x=35+10` =

`-5x=45`

Divide both sides by `-5`.

`x=45/(-5)` =

`x=-9`