Question

How do you solve `|- 4+ 5x | = 15`?

Answer 1

See full solution process below in the Explanation

Explanation:

Because this equation contains an absolute value function we need to compute two different solutions.

Because the absolute value function takes and negative or positive term and converts it to a positive term we must solve the term within the absolute value for both the negative positive form of the equation.

Solution 1)

`-4 + 5x = -15`

`-4 + color(red)(4) + 5x = -15 + color(red)(4)`

`0 + 5x = -11`

`5x = -11`

`(5x)/color(red)(5) = (-11)/color(red)(5)`

`(color(red)(cancel(color(black)(5)))x)/cancel(color(red)(5)) = -11/color(red)(5)`

`x = -11/color(red)(5)` or `-2.2`

Solution 2)

`-4 + 5x = 15`

`-4 + color(red)(4) + 5x = 15 + color(red)(4)`

`0 + 5x = 19`

`5x = 19`

`(5x)/color(red)(5) = 19/color(red)(5)`

`(color(red)(cancel(color(black)(5)))x)/cancel(color(red)(5)) = 19/color(red)(5)`

`x = 19/color(red)(5)` or `3.8`