# How do you solve abs(15-2x)=8?

Apr 6, 2017

$x = \frac{7}{2} \text{ or } x = \frac{23}{2}$

#### Explanation:

There are 2 possible solutions to this type of equation.

Removing the 'bars' gives.

$15 - 2 x = \textcolor{red}{\pm} 8$

• " solve " 15-2x=color(red)(+)8

subtract 15 to both sides.

$\cancel{15} \cancel{- 15} - 2 x = 8 - 15$

$\Rightarrow - 2 x = - 7$

divide both side by - 2

$\frac{\cancel{- 2} x}{\cancel{- 2}} = \frac{- 7}{- 2}$

$\Rightarrow x = \frac{7}{2}$

• " solve " 15-2x=color(red)(-)8

$\Rightarrow - 2 x = - 23$

$\Rightarrow x = \frac{23}{2}$

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

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

$| 15 - 2 \times \frac{7}{2} | = | 8 | = 8$

$| 15 - 2 \times \frac{23}{2} | = | - 8 | = 8$

$\Rightarrow x = \frac{7}{2} \text{ or " x=23/2" are the solutions}$