# How do you solve abs(5x)+5=45?

Feb 1, 2017

$x + \pm 8$

#### Explanation:

$\text{equations involving the" color(blue)" absolute value}$ have 2 possible solutions.

Isolate the absolute value.

subtract 5 from both sides of the equation.

$| 5 x | \cancel{+ 5} \cancel{- 5} = 45 - 5$

$\Rightarrow | 5 x | = 40$

The 2 solutions are obtained by solving $5 x = \textcolor{red}{\pm} 40$

$\textcolor{b l u e}{\text{Solution 1}}$

$\text{solve } 5 x = 40 \Rightarrow x = 8$

$\textcolor{b l u e}{\text{Solution 2}}$

$\text{solve } 5 x = - 40 \Rightarrow x = - 8$

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

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

x=8to|5xx8|+5=|40|+5=40+5 =45 color(white)(xx) ✔︎

$x = - 8 \to | 5 \times - 8 | + 5 = | - 40 | + 5 = 40 + 5 = 45$

$\Rightarrow x = \pm 8 \text{ are the solutions}$