Answer
The solutions are $k=6$ and $k=-\frac{2}{5}$.
Work Step by Step
The given equation is
$\Rightarrow |3k-2|=2|k+2|$
Write the two related linear equations.
$3k-2=2(k+2)$ ...... (1)
$3k-2=2[-(k+2)]$ ...... (2)
Solve equation (1).
$\Rightarrow 3k-2=2(k+2)$
Use distributive property.
$\Rightarrow 3k-2=2k+4$
Add $2-2k$ to each side.
$\Rightarrow 3k-2+2-2k=2k+4+2-2k$
Simplify.
$\Rightarrow k=6$
Check : $k=6$
$\Rightarrow |3k-2|=2|k+2|$
$\Rightarrow |3(6)-2|=2|6+2|$
$\Rightarrow |18-2|=2|8|$
$\Rightarrow |16|=2|8|$
$\Rightarrow 16=16$
True.
Solve equation (2).
$\Rightarrow 3k-2=2[-(k+2)]$
$\Rightarrow 3k-2=-2(k+2)$
Use distributive property.
$\Rightarrow 3k-2=-2k-4$
Add $2+2k$ to each side.
$\Rightarrow 3k-2+2+2k=-2k-4+2+2k$
Simplify.
$\Rightarrow 5k=-2$
Divide each side by $5$.
$\Rightarrow \frac{5k}{5}=-\frac{2}{5}$
Simplify.
$\Rightarrow k=-\frac{2}{5}$
Check : $k=-\frac{2}{5}$
$\Rightarrow |3k-2|=2|k+2|$
$\Rightarrow |3(-\frac{2}{5})-2|=2|-\frac{2}{5}+2|$
$\Rightarrow |-\frac{6}{5}-2|=2|-\frac{2}{5}+2|$
$\Rightarrow |\frac{-6-10}{5}|=2|\frac{-2+10}{5}|$
$\Rightarrow |\frac{-16}{5}|=2|\frac{8}{5}|$
$\Rightarrow \frac{16}{5}=2(\frac{8}{5})$
$\Rightarrow \frac{16}{5}=\frac{16}{5}$
True.
Hence, the solutions are $k=6$ and $k=-\frac{2}{5}$.
