Does anyone know how to do this?

Question

solve the inequality and express the solutions in terms of intervals.
-2< I x I <4

I know the answer should be (-4, 4) but I don't know how they got that answer. Please help!

Answer 1

|x| means the absolute value, by definition it is always greater or equal to zero, so the requirement of |x| being greater than -2 is always satisfied.
Now, you need to have |x| to be smaller than 4, so it must be smaller than 4, and has to be greater than -4, since |-4| = |4| = 4

Answer 2

Solve for x.

-2 < | x | < 4

The absolute value of anything is either positive or zero. So we can rewrite this as:

0 ≤ | x | < 4

Now we can write:

-4 < x < 4

Expressed in interval form, x is in the interval (-4, 4).

The -2 had nothing to do with it. It was just to throw you off. The left side can be disregarded if it is negative.

Answer 3

I do not know if your answer is correct
-2 I x I < 4 means x value is less than 4 and positive
Therfor I think answer well be
x = ( 0,1,2,3 )

Answer 4

It's something of a trick question. |x| is by definition greater than or equal to zero, so the left-hand limit is irrelevant so long as it's negative. So it reduces to |x|<4.