Answer
The solutions of the equation are $x=-4$ and $x=0$.
The graph is shown below.
Work Step by Step
The given equation is
$\Rightarrow |2x+2|=|x-2|$
Write related linear equations.
$\Rightarrow 2x+2=x-2$ ...... (1)
$\Rightarrow 2x+2=-(x-2)$ ...... (2)
Solve equation (1).
$\Rightarrow 2x+2=x-2$
Write a system of linear equations using each side of the original equation.
$\Rightarrow y=2x+2$
$\Rightarrow y=x-2$
By using graphing calculator graph the system.
The intersection point is $(-4,-6)$.
Check:
$\Rightarrow 2x+2=x-2$
$\Rightarrow 2(-4)+2=-4-2$
$\Rightarrow -8+2=-4-2$
$\Rightarrow -6=-6$
True.
Solve equation (2).
$\Rightarrow 2x+2=-(x-2)$
Write a system of linear equations using each side of the original equation.
$\Rightarrow y=2x+2$
$\Rightarrow y=-(x-2)$
By using graphing calculator graph the system.
The intersection point is $(0,2)$.
Check:
$\Rightarrow 2x+2=-(x-2)$
$\Rightarrow 2(0)+2=-(0-2)$
$\Rightarrow 0+2=2$
$\Rightarrow 2=2$
True.
Hence, the solutions of the equation are $x=-4$ and $x=0$.
