Answer
The solutions are $r=3$ and $r=\frac{1}{2}$.
The graph is shown below.
Work Step by Step
The given equation is
$\Rightarrow |r+2|=|3r-4|$
Write the two related linear equations.
$r+2=3r-4$ ...... (1)
$r+2=-(3r-4)$ ...... (2)
Solve equation (1).
$\Rightarrow r+2=3r-4$
Add $4-r$ to each side.
$\Rightarrow r+2+4-r=3r-4+4-r$
Simplify.
$\Rightarrow 6=2r$
Divide each side by $2$.
$\Rightarrow \frac{6}{2}=\frac{2r}{2}$
Simplify.
$\Rightarrow 3=r$
Solve equation (2).
$\Rightarrow r+2=-(3r-4)$
Use distributive property.
$\Rightarrow r+2=-3r+4$
Add $3r-2$ to each side.
$\Rightarrow r+2+3r-2=-3r+4+3r-2$
Simplify.
$\Rightarrow 4r=2$
Divide each side by $4$.
$\Rightarrow \frac{4r}{4}=\frac{2}{4}$
Simplify.
$\Rightarrow r=\frac{1}{2}$
Hence, the solutions are $r=3$ and $r=\frac{1}{2}$.
