# How do you solve abs(2g-5)=9?

May 9, 2018

$g = 7 \mathmr{and} - 2$

#### Explanation:

Due to how $\left\mid \right\mid$ works, both the positive and negative of the function can be taken, so:
$2 g - 5 = 9$ or $- \left(2 g - 5\right) = 9$, $2 g - 5 = - 9$

$2 g = 14 \mathmr{and} 2 g = - 4$

$g = 7 \mathmr{and} - 2$

May 9, 2018

$g = - 2 \text{ or } g = 7$

#### Explanation:

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

$2 g - 5 = 9 \leftarrow \textcolor{m a \ge n t a}{\text{positive value}}$

$\text{add 5 to both sides and divide by 2}$

$\Rightarrow 2 g = 9 + 5 = 14 \Rightarrow g = \frac{14}{2} = 7$

$- \left(2 g - 5\right) = 9 \leftarrow \textcolor{m a \ge n t a}{\text{negative value}}$

$\Rightarrow - 2 g + 5 = 9$

$\text{subtract 5 from both sides and divide by } - 2$

$\Rightarrow - 2 g = 9 - 5 = 4 \Rightarrow g = \frac{4}{- 2} = - 2$

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

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

$g = 7 \to | 14 - 5 | = | 9 | = 9$

$g = - 2 \to | - 4 - 5 | = | - 9 | = 9$

$\Rightarrow g = - 2 \text{ or "g=7" are the solutions}$