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

Apr 17, 2018

$x > - 6$, $x < 14$

#### Explanation:

$| - 2 x + 8 | < 20$

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

$\cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot$

$- \left(- 2 x + 8\right) < 20$

$- 2 x + 8 > - 20$

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

$- 2 x > - 20 - 8$

$- x > - \frac{28}{2}$

$x < 14$

$\cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot$

$- 2 x + 8 < 20$

$- 2 x < 20 - 8$

$- 2 x < 12$

$- x < 6$

$x > - 6$

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!