Question

How do you solve `-|x+1|=-2`?

Answer 1

See the entire solution process below:

Explanation:

First, multiply each side of the equation by `color(red)(-1)` to isolate the absolute value term while keeping the equation balanced:

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

`abs(x + 1) = 2`

The absolute value function takes any negative or positive term and transforms it into its positive form. Therefore the term within the absolute value function must be solved for both the negative and positive form of the term it is equated to.

Solution 1)

`x + 1 = -2`

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

`x + 0 = -3`

`x = -3`

Solution 2)

`x + 1 = 2`

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

`x + 0 = 1`

`x = 1`

The solutions to this problem are:

`x = -3` and `x = 1`