Solve: −3 |1−2/3v| = −9

Mathematics

2 answers:

My name is Ann [436]2 years ago

4 0

Answer: v = -3, v = 6

<u>Step-by-step explanation:</u>

$-3\bigg|1-\dfrac{2}{3}v\bigg|=-9\\\\\\\text{Divide both sides by -3}\quad \longrightarrow \quad \bigg|1-\dfrac{2}{3}v\bigg|=3\\\\\\\text{Separate into 2 equations: one for positive and the other for negative}\\\\\qquad \underline{\qquad\text{positive}\qquad}\qquad \qquad \qquad \qquad \underline{\quad \text{negative}\quad }\\.\quad 1-\dfrac{2}{3}v=3\qquad}\qquad \qquad \qquad \qquad 1-\dfrac{2}{3}v=-3\\\\\\.\qquad \qquad \qquad \text{Substract 1 from all sides}$

$.\qquad -\dfrac{2}{3}v=2\qquad}\qquad \qquad \qquad \qquad -\dfrac{2}{3}v=-4\\\\\\\\.\qquad \qquad \qquad \text{Multiply all sides by }-\dfrac{3}{2}\\\\.\quad -\dfrac{2}{3}v\bigg(-\dfrac{3}{2}\bigg)=2\bigg(-\dfrac{3}{2}\bigg)\qquad}\qquad -\dfrac{2}{3}v\bigg(-\dfrac{3}{2}\bigg)=-4\bigg(-\dfrac{3}{2}\bigg)\\\\\\.\quad \qquad \large\boxed{v=-3}\qquad \qquad \qquad \qquad \quad \large\boxed{v=6}$