# Solve |2x+1| <= |x-3| for x

Gold Member
$$\left| {2x + 1} \right| \ge \left| {x - 3} \right|$$

Now, i must solve for x. I could easily do it by graphing it on my calculator, and get an answer of $$x \le - 4,x \ge \frac{2}{3}$$.

How can i do it algebraically?

Dan.

Last edited:

AlephZero
Homework Helper
You could start by finding the points where |2x+1| = |x+3|

You can get rid of the absolute values by squaring each side.

HallsofIvy