# How do you solve absolute value inequalities with absolute value variables on both sides #abs(2x)<=abs(x-3)#?

##### 1 Answer

Apr 7, 2015

All values of x in the interval [-3,2]

To remove the absolute value sign, square both sides, so that both would be positive only. Accordingly,

4

4

3

(x+3)(x-2)

Now, there can be two options for this inequality to hold good.

Case 1 x+3 is positive, that is x

Case 2 x+3 is negative, that is x

To understand the solution mark the above inequalities on the number line. The solution to the inequality would be x