# How do you solve y=abs(2x+3)?

May 1, 2015

Assuming that all you require to "solve" this equation is to state it without the absolute value operation:

If $2 x + 3 < 0$
$\rightarrow x < - \frac{3}{2}$
then
$y = \left\mid 2 x + 3 \right\mid$
$\rightarrow y = - 2 x - 3$

If $2 x + 3 \ge 0$
$\rightarrow x \ge - \frac{3}{2}$
then
$y = \left\mid 2 x + 3 \right\mid$
$\rightarrow y = 2 x + 3$

Therefore
$y = \left\mid 2 x + 3 \right\mid \left\{\begin{matrix}\equiv y = - 2 x - 3 \text{ if " x<-3/2 \\ -=y=2x+3 " if } x \ge - \frac{3}{2}\end{matrix}\right.$