Answer
$x=17$ and $x=\frac{7}{5}$
Work Step by Step
The given equation is
$\Rightarrow 3|x-4|=|2x+5|$
Write related linear equations.
$\Rightarrow 3(x-4)=2x+5$ or $3(x-4)=−(2x+5)$
Solve the first equation.
$\Rightarrow 3(x-4)=2x+5$
Use distributive property.
$\Rightarrow 3x-12=2x+5$
Add $-2x+12$ to each side.
$\Rightarrow 3x-12-2x+12=2x+5-2x+12$
Simplify.
$\Rightarrow x=17$
Solve the second equation.
$\Rightarrow 3(x-4)=-(2x+5)$
Use distributive property.
$\Rightarrow 3x-12=-2x-5$
Add $2x+12$ to each side.
$\Rightarrow 3x-12+2x+12=-2x-5+2x+12$
Simplify.
$\Rightarrow 5x=7$
Divide each side by $5$.
$\Rightarrow \frac{5x}{5}=\frac{7}{5}$
Simplify.
$\Rightarrow x=\frac{7}{5}$
Check $x=17$
$\Rightarrow 3|17-4|=|2(17)+5|$
$\Rightarrow 3|13|=|34+5|$
$\Rightarrow 3(13)=|39|$
$\Rightarrow 39=39$
True.
Check $x=-3$
$\Rightarrow 3|\frac{7}{5}-4|=|2(\frac{7}{5})+5|$
$\Rightarrow 3|\frac{7-20}{5}|=|\frac{14}{5}+5|$
$\Rightarrow 3|-\frac{13}{5}|=|\frac{14+25}{5}|$
$\Rightarrow 3(\frac{13}{5})=|\frac{39}{5}|$
$\Rightarrow \frac{39}{5}=\frac{39}{5}$
True.
Hence, the solutions are $x=17$ and $x=\frac{7}{5}$.
