Answer
The solutions of the equation are $x=13$ and $x=1$.
Work Step by Step
The given equation is
$\Rightarrow |2x-8|=|x+5|$
Write related linear equations.
$\Rightarrow 2x-8=x+5$ ...... (1)
$\Rightarrow 2x-8=-(x+5)$ ...... (2)
Solve equation (1).
$\Rightarrow 2x-8=x+5$
Write a system of linear equations using each side of the original equation.
$\Rightarrow y=2x-8$
$\Rightarrow y=x+5$
By using graphing calculator graph the system.
The intersection point is $(13,18)$.
Check:
$\Rightarrow |2x-8|=|x+5|$
$\Rightarrow |2(13)-8|=|13+5|$
$\Rightarrow |26-8|=|18|$
$\Rightarrow |18|=|18|$
True.
Solve equation (2).
$\Rightarrow 2x-8=-(x+5)$
Write a system of linear equations using each side of the original equation.
$\Rightarrow y=2x-8$
$\Rightarrow y=-(x+5)$
By using graphing calculator graph the system.
The intersection point is $(1,-6)$.
Check:
$\Rightarrow |2x-8|=|x+5|$
$\Rightarrow |2(1)-8|=|1+5|$
$\Rightarrow |2-8|=|6|$
$\Rightarrow |-6|=|6|$
$\Rightarrow 6=6$
True.
Hence, the solutions of the equation are $x=13$ and $x=1$.
