How do you solve an absolute value inequality?

|2x|

Question

How do you solve an absolute value inequality?

|2x|<=|x-3|

anonymous · Answer

x -3 ≥ 2x          
Can you solve it?

anonymous · Answer

I solved both $$2x \le x-3$$ and 
$$2x \ge  -(x-3)$$

anonymous · Answer

Exactly right :)
Absolute value always yields 2 results

anonymous · Answer

However when I check my answers, $$x \le-3 $$ and $$x \ge 1$$ Everything get's all weird because I know that -2 works as a solution, and 0 works too.

anonymous · Answer

You check the result x = -2?

anonymous · Answer

I did, it turns out to be $$4\le5$$

anonymous · Answer

Then double check your post!

anonymous · Answer

but my requirements after I solved were that $$x \le -3$$ and x being -2 doesn't fulfill the requirement.

anonymous · Answer

Your solving is correct, but it's likely that you write the question wrong somewhere :(

anonymous · Answer

It seems to me that the question is:
| 2x |  ≥ | x -3 |
=> The result is  x ≥ -3 and x ≤ 1
Then your book solution is match with  the interval -3 ≤ x ≤ 1

directrix · Answer

In interval notation, I got a solution of [-3, 1 ]. -2 is contained in that interval.

anonymous · Answer

HELLO... YOU CAN WRITE$$4x ^{2}\le(x-3)^{2}$$