Question

How do you solve `|-2x + 8| <20`?

Answer 1

`x > -6`, `x < 14`

Explanation:

`| -2x+8 | < 20`

We can have solutions, where the terms inside the absolute value is `-(-2x+8)` or `(-2x+8)`. So we need to solve for both of these

`* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *`

`-( -2x+8 ) < 20`

`-2x + 8 > -20`

note that the sign changed direction. This occurs anytime we multiply or divide by a negative number

`-2x > -20 - 8`

`-x > -28/2`

`x < 14`

`* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *`

`-2x + 8 < 20`

`-2x < 20-8`

`-2x < 12`

`-x < 6`

`x > -6`

To check our work, let's graph the original function and see if it is less than `14` and greater than `-6`

Yep, it is, so we were right!