Question

How do you solve `4|-6x + 6| + -3 = 93`?

Answer 1

`x = -3` and `x = 5`

Explanation:

When solving an absolute value problem the first step is to isolate the absolute value on one side of the equation:

`4abs(-6x + 6) + -3 + 3 = 93 + 3`

`4abs(-6x + 6) + 0 = 96`

`4abs(-6x + 6) = 96`

`(4abs(-6x + 6))/4 = 96/4`

`(cancel(4)abs(-6x + 6))/cancel(4) = 24`

`abs(-6x + 6) = 24`

Now because the absolute value function converts both negative and positive numbers to a negative number we must solve the term within the absolute value for both `24` and `-24`:

`-6x + 6 = 24`

`-6x + 6 - 6 = 24 - 6`

`-6x + 0 = 18`

`-6x = 18`

`(-6x)/-6 = 18/(-6)`

`(cancel(-6)x)/cancel(-6) = -3`

`x = -3`

and

`-6x + 6 = -24`

`-6x + 6 - 6 = -24 - 6`

`-6x + 0 = -30`

`-6x = -30`

`(-6x)/-6 = (-30)/(-6)`

`(cancel(-6)x)/cancel(-6) = 5`

`x = 5`