Answer
$x=6$ and $x=−2$
Work Step by Step
The given equation is
$\Rightarrow |x−2|+5=9$
Subtract $5$ from each side.
$\Rightarrow |x−2|+5-5=9-5$
Simplify.
$\Rightarrow |x−2|=4$
Write related linear equations.
$\Rightarrow x−2=4$ or $x−2=−4$
Add $2$ to each side.
$\Rightarrow x−2+2=4+2$ or $x−2+2=−4+2$
Simplify.
$\Rightarrow x=6$ or $x=−2$
Check $x=6$
$\Rightarrow |6−2|+5=9$
$\Rightarrow |4|+5=9$
$\Rightarrow 4+5=9$
$\Rightarrow 9=9$
True.
Check $x=-2$
$\Rightarrow |-2−2|+5=9$
$\Rightarrow |-4|+5=9$
$\Rightarrow 4+5=9$
$\Rightarrow 9=9$
True.
Hence, the solutions are $x=6$ and $x=−2$.
