Answer
The solutions are $x=-5$ and $x=3$.
Work Step by Step
The given equation is
$\Rightarrow |3x-45|=|12x|$
Write related linear equations.
$\Rightarrow 3x-45=12x$ or $3x-45=−12x$
Solve the first equation.
$\Rightarrow 3x-45=12x$
Subtract $3x$ from each side.
$\Rightarrow 3x-45-3x=12x-3x$
Simplify.
$\Rightarrow -45=9x$
Divide each side by $9$.
$\Rightarrow \frac{-45}{9}=\frac{9x}{9}$
Simplify.
$\Rightarrow -5=x$
Solve the second equation.
$\Rightarrow 3x-45=-12x$
Subtract $3x$ from each side.
$\Rightarrow 3x-45-3x=-12x-3x$
Simplify.
$\Rightarrow -45=-15x$
Divide each side by $-15$.
$\Rightarrow \frac{-45}{-15}=\frac{-15x}{-15}$
Simplify.
$\Rightarrow 3=x$
Check $x=-5$
$\Rightarrow |3x-45|=|12x|$
$\Rightarrow |3(-5)-45|=|12(-5)|$
$\Rightarrow |-15-45|=|-60|$
$\Rightarrow |-60|=|-60|$
$\Rightarrow 60=60$
True.
Check $x=3$
$\Rightarrow |3x-45|=|12x|$
$\Rightarrow |3(3)-45|=|12(3)|$
$\Rightarrow |9-45|=|36|$
$\Rightarrow |-36|=|36|$
$\Rightarrow 36=36$
True.
Hence, the solutions are $x=-5$ and $x=3$.
