Question

Solve: −3 |1−2/3v| = −9

Answer 1

Answer: v = -3 or 6

Explanation:

Answer 2

Answer: v = -3, v = 6

Explanation:

`-3\bigg|1-(2)/(3)v\bigg|=-9\\\\\\\text{Divide both sides by -3}\quad \longrightarrow \quad \bigg|1-(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-(2)/(3)v=3\qquad}\qquad \qquad \qquad \qquad 1-(2)/(3)v=-3\\\\\\.\qquad \qquad \qquad \text{Substract 1 from all sides}`

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