Answer
$x=1$ and $x=\frac{1}{2}$
Work Step by Step
The given equation is
$\Rightarrow |3x-2|=x$
Write related linear equations.
$\Rightarrow 3x−2=x$ or $3x−2=−x$
Solve the first equation.
$\Rightarrow 3x−2=x$
Add $2-x$ to each side.
$\Rightarrow 3x−2+2-x=x+2-x$
Simplify.
$\Rightarrow 2x=2$
Divide each side by $2$.
$\Rightarrow \frac{2x}{2}=\frac{2}{2}$
Simplify.
$\Rightarrow x=1$
Solve the second equation.
$\Rightarrow 3x−2=-x$
Add $2+x$ to each side.
$\Rightarrow 3x−2+2+x=-x+2+x$
Simplify.
$\Rightarrow 4x=2$
Divide each side by $4$.
$\Rightarrow \frac{4x}{4}=\frac{2}{4}$
Simplify.
$\Rightarrow x=\frac{1}{2}$
Check $x=1$
$\Rightarrow |3(1)-2|=1$
$\Rightarrow |3-2|=1$
$\Rightarrow |1|=1$
$\Rightarrow 1=1$
True.
Check $x=\frac{1}{2}$
$\Rightarrow |3(\frac{1}{2})-2|=\frac{1}{2}$
$\Rightarrow |\frac{3}{2}-2|=\frac{1}{2}$
$\Rightarrow |\frac{3-4}{2}|=\frac{1}{2}$
$\Rightarrow |-\frac{1}{2}|=\frac{1}{2}$
$\Rightarrow \frac{1}{2}=\frac{1}{2}$
True.
Hence, the solutions are $x=1$ and $x=\frac{1}{2}$.
