Chapter 2.5, Problem 37E

To determine

To solve:The given equation.

Answer to Problem 37E

Here, the equation $|r+2|=|3r-4|$ is $r=3orr=\frac{5}{2}$ .

Explanation of Solution

Given: $|r+2|=|3r-4|$

Calculation:

Given

  $|r+2|=|3r-4|$

Write two related linear equations

  $r+2=3r-4orr+2=-\left(3r-4\right)$

Solve equation 1:

  $r+2=3r-4$

Subtract both sides by $3r$

  $r-3r+2=3r-3r-4$

Subtract both sides by $2$

  $-2r+2-2=-4-2$

Divide both sides by $-2$

  $\begin{array}{l}\frac{-2r}{-2}=\frac{-6}{-2}\\ r=3\end{array}$

Solve equation 2:

  $r+2=-\left(3r-4\right)$

Use Distributive Property

  $r+2=-3r+4$

Add both sides by $3r$

  $r+2+3r=-3r+3r+4$

Subtract both sides by $2$

  $4r+2-2=4-2$

Divide both sides by $4$

  $\begin{array}{l}\frac{4r}{4}=\frac{2}{4}\\ r=\frac{1}{2}\end{array}$

Check $\left(r=3\right)$ :

  $|r+2|=|3r-4|$

Substitute

  $|\left(3\right)+2|=|3\left(3\right)-4|$

Simplify

  $\left|5\right|=|9-4|$

Simplify

  $\left|5\right|=\left|5\right|$

Get absolute value

  $5=5$

Check $(r=\frac{1}{2})$ :

  $|r+2|=|3r-4|$

Substitute

  $|(\frac{1}{2})+2|=|3(\frac{1}{2})-4|$

Simplify

  $|\frac{1}{2}+\frac{4}{2}|=|\frac{3}{2}-\frac{8}{2}|$

Simplify

  $\left|\frac{5}{2}\right|=|-\frac{5}{2}|$

Get absolute value

  $\frac{5}{2}=\frac{5}{2}$

Its graph would be :

  $r=3orr=\frac{5}{2}$

Conclusion:

Therefore, the equation $|r+2|=|3r-4|$ is $r=3orr=\frac{5}{2}$ .