Answer
The solutions are $w=-2$ and $w=-\frac{1}{5}$.
Work Step by Step
The given equation is
$\Rightarrow 2|4w-1|=3|4w+2|$
Write the two related linear equations.
$2(4w-1)=3(4w+2)$ ...... (1)
$2(4w-1)=3[-(4w+2)]$ ...... (2)
Solve equation (1).
$\Rightarrow 2(4w-1)=3(4w+2)$
Use distributive property.
$\Rightarrow 8w-2=12w+6$
Add $-8w-6$ to each side.
$\Rightarrow 8w-2-8w-6=12w+6-8w-6$
Simplify.
$\Rightarrow -8=4w$
Divide each side by $4$.
$\Rightarrow \frac{-8}{4}=\frac{4w}{4}$
Simplify.
$\Rightarrow -2=w$
Check : $w=-2$
$\Rightarrow 2|4w-1|=3|4w+2|$
$\Rightarrow 2|4(-2)-1|=3|4(-2)+2|$
$\Rightarrow 2|-8-1|=3|-8+2|$
$\Rightarrow 2|-9|=3|-6|$
$\Rightarrow 2(9)=3(6)$
$\Rightarrow 18=18$
True.
Solve equation (2).
$\Rightarrow 2(4w-1)=3[-(4w+2)]$
Use distributive property.
$\Rightarrow 8w-2=-12w-6$
Add $12w+2$ to each side.
$\Rightarrow 8w-2+12w+2=-12w-6+12w+2$
Simplify.
$\Rightarrow 20w=-4$
Divide each side by $20$.
$\Rightarrow \frac{20w}{20}=\frac{-4}{20}$
Simplify.
$\Rightarrow w=-\frac{1}{5}$
Check : $w=-\frac{1}{5}$
$\Rightarrow 2|4w-1|=3|4w+2|$
$\Rightarrow 2|4(-\frac{1}{5})-1|=3|4(-\frac{1}{5})+2|$
$\Rightarrow 2|-\frac{4}{5}-1|=3|-\frac{4}{5}+2|$
$\Rightarrow 2|\frac{-4-5}{5}|=3|\frac{-4+10}{5}|$
$\Rightarrow 2|\frac{-9}{5}|=3|\frac{6}{5}|$
$\Rightarrow 2(\frac{9}{5})=3(\frac{6}{5})$
$\Rightarrow \frac{18}{5}=\frac{18}{5}$
True.
Hence, the solutions are $w=-2$ and $w=-\frac{1}{5}$.
