How do you solve 2abs(3x - 2 ) = 14?

Jun 28, 2015

${x}_{1} = 3$

${x}_{2} = - \frac{5}{3}$

Explanation:

$2 \left\mid 3 x - 2 \right\mid = 14 \rightarrow \left\mid 3 x - 2 \right\mid = 7$

Knowing that $\left\mid x \right\mid = \left\mid - x \right\mid$ we now have two possibilities:

$3 x - 2 = 7$ or
$3 x - 2 = - 7$

I) $3 x - 2 = 7 \rightarrow 3 x = 7 + 2 = 9 \rightarrow x = \frac{9}{3} = 3$

II)$3 x - 2 = - 7 \rightarrow 3 x = - 7 + 2 = - 5 \rightarrow x = - \frac{5}{3}$