# How do you solve 3|3q-2|=21?

##### 1 Answer
Feb 9, 2017

$q = 3 \text{ or } q = - \frac{5}{3}$

#### Explanation:

Isolate the $\textcolor{b l u e}{\text{absolute value}}$ by dividing both sides of the equation by 3

${\cancel{3}}^{1} / {\cancel{3}}^{1} | 3 q - 2 | = \frac{21}{3}$

$\Rightarrow | 3 q - 2 | = 7$

There are 2 solutions to the equation.

$\text{Solve } 3 q - 2 = \textcolor{red}{\pm} 7$

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

$3 q - 2 = \textcolor{red}{+ 7} \Rightarrow 3 q = 7 + 2 = 9 \Rightarrow q = \frac{9}{3} = 3$

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

$3 q - 2 = \textcolor{red}{- 7} \Rightarrow 3 q = - 7 + 2 = - 5 \Rightarrow q = - \frac{5}{3}$

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

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

• x=3to3|9-2|=3xx7=21

• x=-5/3to3|-5-2|=3xx|-7|=3xx7=21

$\Rightarrow x = 3 \text{ or " x=-5/3" are the solutions}$