# How do you solve 2abs(6-2x)-1=7?

Oct 16, 2016

$x = 1$ and $x = 5$

#### Explanation:

$2 \left\mid 6 - 2 x \right\mid - 1 = 7$

Isolate the absolute value part of the equation.

$2 \left\mid 6 - 2 x \right\mid - 1 = \textcolor{w h i t e}{a} 7$
$\textcolor{w h i t e}{a a a a a a {a}^{2}} + 1 \textcolor{w h i t e}{a} + 1 \textcolor{w h i t e}{a a a}$Add 1 to both sides

$\frac{2 \left\mid 6 - 2 x \right\mid}{2} \textcolor{w h i t e}{{a}^{2} a} = \textcolor{w h i t e}{a} \frac{8}{2} \textcolor{w h i t e}{a a a}$Divide both sides by 2

$\left\mid 6 - 2 x \right\mid = 4$

Solving absolute value problems requires setting up TWO equations. Make the right side of the 2nd equation negative.

$\textcolor{w h i t e}{{a}^{2}} 6 - 2 x = 4 \textcolor{w h i t e}{a a a}$and$\textcolor{w h i t e}{a a a} 6 - 2 x = - 4$
$- 6 \textcolor{w h i t e}{a a a a a} - 6 \textcolor{w h i t e}{a a a a a a} - 6 \textcolor{w h i t e}{a a a a a {a}^{2} a} - 6 \textcolor{w h i t e}{a a}$Subtract 6

$\frac{- 2 x}{-} 2 = \frac{- 2}{-} 2 \textcolor{w h i t e}{a a a}$and$\textcolor{w h i t e}{a a} \frac{- 2 x}{-} 2 = \frac{- 10}{-} 2 \textcolor{w h i t e}{a a}$Divide by -2

$\textcolor{w h i t e}{a a} x = 1 \textcolor{w h i t e}{a a a a a a a}$and$\textcolor{w h i t e}{a a a a a a} x = 5$