## Big Ideas Math - Algebra 1, A Common Core Curriculum

The solutions of the equation are $x=-4$ and $x=0$. The graph is shown below.
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 $x=0$.