# How do you solve 8abs(x+7)-3=5?

May 3, 2018

$x = - 8 \text{ or } x = - 6$

#### Explanation:

$\text{the expression inside the absolute value bars can be}$
$\text{positive or negative hence we have to consider both}$

$\text{isolate "|x+7|" by adding 3 to both sides}$

$8 | x + 7 | \cancel{- 3} \cancel{+ 3} = 5 + 3$

$\Rightarrow 8 | x + 7 | = 8$

$\text{divide both sides by 8}$

$\frac{\cancel{8}}{\cancel{8}} | x + 7 | = \frac{8}{8}$

$\Rightarrow | x + 7 | = 1$

$\text{consider the "color(magenta)" positive value ""of } x + 7$

$\Rightarrow x + 7 = 1 \leftarrow \text{subtract 7 from both sides}$

$\Rightarrow x = 1 - 7 = - 6$

$\text{consider the "color(magenta)"negative value ""of } x + 7$

$\Rightarrow - \left(x + 7\right) = 1 \leftarrow \text{distribute}$

$\Rightarrow - x - 7 = 1 \leftarrow \text{add 7 to both sides}$

$\Rightarrow - x = 1 + 7 = 8$

$\Rightarrow x = - 8$

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

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

$x = - 6 \to 8 | - 6 + 7 | - 3 = 8 - 3 = 5$

$x = - 8 \to 8 | - 8 + 7 | - 3 = 8 | - 1 | - 3 = 8 - 3 = 5$

$\Rightarrow x = - 8 \text{ or "x=-6" are the solutions}$