# How do you solve - 2abs(x - 3) + 10 = - 4?

Feb 8, 2017

$x = 10 \text{ or } x = - 4$

#### Explanation:

Isolate the $\textcolor{b l u e}{\text{absolute value}}$

subtract 10 from both sides.

$- 2 | x - 3 | \cancel{+ 10} \cancel{- 10} = - 4 - 10$

$\Rightarrow - 2 | x - 3 | = - 14$

divide both sides by - 2

$\frac{\cancel{- 2}}{\cancel{- 2}} | x - 3 | = \frac{- 14}{- 2}$

$\Rightarrow | x - 3 | = 7 \leftarrow \textcolor{red}{\text{absolute value isolated on left}}$

Equations with an absolute value usually have 2 solutions.

We now solve $x - 3 = \textcolor{red}{\pm} 7$

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

$x - 3 = \textcolor{red}{+} 7 \Rightarrow x = 7 + 3 = 10$

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

$x - 3 = \textcolor{red}{-} 7 \Rightarrow x = - 7 + 3 = - 4$

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

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

•x=10to-2|10-3|+10=-14+10=-4

•x=-4to-2|-4-3|+10=-14+10=-4

$\Rightarrow x = 10 \text{ or "x=-4" are the solutions}$