Answer
$-3;6$
Work Step by Step
Given $$-3\left|1 - \frac{2}{3}v\right| = -9.$$
Divide both sides by $-3$ $$\left|1 - \frac{2}{3}v\right| = 3.$$
a) Equate to $3$ $$1 - \frac{2}{3}v = 3.$$
Subtract $1$ from both sides $$- \frac{2}{3}v = 2.$$
Multiply both sides by $3$ $$-2v = 6.$$
Divide both sides by $-2$ $$v = -3.$$
b) Equate to $-3$ $$1 - \frac{2}{3}v = -3.$$
Subtract $1$ from both sides $$- \frac{2}{3}v = -4.$$
Multiply both sides by $3$ $$-2v = -12.$$
Divide both sides by $-2$ $$v = 6.$$
Hence the solutions are $-3$ and $6$.
