# How do you solve abs(2x - 6) = 12?

Apr 8, 2018

$x = - 3 , 9$

#### Explanation:

$2 x - 6 = 12 \mathmr{and} 2 x - 6 = - 12$

$2 x = 18 \mathmr{and} 2 x = - 6$

$x = 9 \mathmr{and} x = - 3$

Apr 8, 2018

$x = - 3 \text{ or } x = 9$

#### Explanation:

$\text{the expression inside the absolute value can be positive}$
$\text{or negative, thus there are 2 possible solutions}$

$\textcolor{m a \ge n t a}{\text{Positive value}}$

$2 x - 6 = 12$

$\text{add 6 to both sides}$

$\Rightarrow 2 x = 18 \Rightarrow x = 9$

$\textcolor{m a \ge n t a}{\text{Negative value}}$

$- \left(2 x - 6\right) = 12$

$\Rightarrow - 2 x + 6 = 12$

$\text{subtract 6 from both sides}$

$\Rightarrow - 2 x = 6$

$\text{divide both sides by } - 2$

$\Rightarrow x = - 3$

$\textcolor{b l u e}{\text{As a check}}$

Substitute these values into the left side and if equal to the right side then they are the solutions.

$| \left(2 \times 9\right) - 6 | = | 18 - 6 | = | 12 | = 12$

$| \left(2 \times - 3\right) - 6 | = | - 6 - 6 | = | - 12 | = 12$

$\Rightarrow x = - 3 \text{ or "x=9" are the solutions}$