How do you solve for x: −5|3x − 2| = −15?

May 10, 2017

$x = - \frac{1}{3} \text{ or } x = \frac{5}{3}$

Explanation:

$\textcolor{b l u e}{\text{Isolate " |3x-5|" by dividing both sides by - 5}}$

$\frac{\cancel{- 5}}{\cancel{- 5}} | 3 x - 2 | = \frac{- 15}{- 5}$

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

$\text{the expression inside the bars can be positive or negative}$

$\text{hence there are 2 possible solutions}$

$\textcolor{red}{\pm} \left(3 x - 2\right) = 3$

$\textcolor{b l u e}{\text{First solution}}$

$3 x - 2 = 3$

$\text{add 2 to both sides}$

$3 x \cancel{- 2} \cancel{+ 2} = 3 + 2$

$\Rightarrow 3 x = 5$

$\text{divide both sides by 3}$

$\frac{\cancel{3} x}{\cancel{3}} = \frac{5}{3}$

$\Rightarrow x = \frac{5}{3}$

$\textcolor{b l u e}{\text{Second solution}}$

$- \left(3 x - 2\right) = 3$

$\Rightarrow - 3 x + 2 = 3$

$\text{subtract 2 from both sides}$

$\Rightarrow - 3 x = 1$

$\text{divide both sides by - 3}$

$\Rightarrow x = - \frac{1}{3}$