We must write the following expression without the absolute value symbol:
[tex]|x+7\left|\right?.[/tex]We have two cases:
1) If (x + 7) ≥ 0 or x ≥ -7, the expression is (x + 7).
2) If (x + 7) < 0 or x < -7, the expression is -(x + 7).
Combining these results, we have:
[tex]|x+7\left|=\right?\begin{cases}x+7\text{ if }x\ge-7 \\ -x-7\text{ if }x<-7\end{cases}[/tex]AnswerThe equivalent expression to |x + 7| without an absolute value symbol is:
[tex]|x+7\left|=\right?\begin{cases}x+7\text{ if }x\ge-7 \\ -x-7\text{ if }x<-7\end{cases}[/tex]