Chapter 3.7, Problem 10P

Solve each equation. If there is no solution, write no solution.

$2=\left|m+\frac{2}{3}\right|$

To determine

To solve: $2=\left|m+\frac{2}{3}\right|$

Answer to Problem 10P

The solution is $m=\frac{4}{3},-\frac{8}{3}$

Explanation of Solution

Given information: $2=\left|m+\frac{2}{3}\right|$

Calculation:

  $2=\left|m+\frac{2}{3}\right|$

  $\begin{array}{l}\Rightarrow 2=m+\frac{2}{3}\\ \Rightarrow m=2-\frac{2}{3}\\ \Rightarrow m=\frac{4}{3}\end{array}$ or $\begin{array}{l}\Rightarrow -2=m+\frac{2}{3}\\ \Rightarrow m=-2-\frac{2}{3}\\ \Rightarrow m=-\frac{8}{3}\end{array}$

Thus, the solution is $m=\frac{4}{3},-\frac{8}{3}$