Question

How do you solve `-5| 5x - 5| = - 75`?

Answer 1

See a solution process below:

Explanation:

First, divide each side of the equation by `color(red)(-5)` to isolate the absolute value function while keeping the equation balanced:

`(-5abs(5x - 5))/color(red)(-5) = (-75)/color(red)(-5)`

`(color(red)(cancel(color(black)(-5)))abs(5x - 5))/cancel(color(red)(-5)) = 15`

`abs(5x - 5) = 15`

The absolute value function takes any term and transforms it to its non-negative form. Therefore, we must solve the term within the absolute value function for both its negative and positive equivalent.

Solution 1:

`5x - 5 = -15`

`5x - 5 + color(red)(5) = -15 + color(red)(5)`

`5x - 0 = -10`

`5x = -10`

`(5x)/color(red)(5) = -10/color(red)(5)`

`(color(red)(cancel(color(black)(5)))x)/cancel(color(red)(5)) = -2`

`x = -2`

Solution 2:

`5x - 5 = 15`

`5x - 5 + color(red)(5) = 15 + color(red)(5)`

`5x - 0 = 20`

`5x = 20`

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

`(color(red)(cancel(color(black)(5)))x)/cancel(color(red)(5)) = 4`

`x = 4`

The Solutions Are: `x = -2` and `x = 4`