Question

How do you solve `-5|x + 1| = -10`?

Answer 1

See the entire solution process below:

Explanation:

First step is to isolate the absolute value terms while keeping the equation balanced by dividing each side of the equation by `color(red)(-5)`:

`(-5abs(x + 1))/color(red)(-5) = (-10)/color(red)(-5)`

`(color(red)(cancel(color(black)(-5)))abs(x + 1))/cancel(color(red)(-5)) =2`

`abs(x + 1) = 2`

The absolute value function transforms any negative or positive number into its positive form. Therefore, to solve this problem we need to solve the term inside the absolute value for both the positive and negative form of what it is equation to. Therefore there will be two solutions.

Solution 1)

`x + 1 = 2`

`x + 1 - color(red)(1) = 2 - color(red)(1)`

`x + 0 = 1`

`x = 1`

Solution 2)

`x + 1 = -2`

`x + 1 - color(red)(1) = -2 - color(red)(1)`

`x + 0 = -3`

`x = -3`