When solving inequalities involving ABSOLUTE VALUE, there are 2 things you need to know:
Rule #1: If |something| < k, then –k < something < k
Rule #2: If |something| > k, then EITHER something > k OR something < -k
Note: these rules assume that k is positive

So, when we apply Rule #1, we get: \(-2 < -\frac{x}{3} + 3 < 2\)

Subtract 3 from all sides of the inequality: \(-5 < -\frac{x}{3} < -1\)

Multiply all sides of the inequality by \(-3\) to get: \(15 > x > 3\)
aside: Since we multiplied buy a NEGATIVE value, we had to REVERSE the direction of the inequality symbols

Or we can write this inequality as: \(3 < x < 15\)

Now let's examine all four answers choices and see which MUST be true.

A. \(x>0\)
If \(3 < x < 15\), then x MUST be greater than 0
So, A must be true.

B. \(x <9\)
If \(3 < x < 15\), then x COULD equal 10
So, B need not be true.

C. \(x > -9\)
If \(3 < x < 15\), then x MUST be greater than -9
So, C must be true

D. \(0<x<3\)
If \(3 < x < 15\), then x COULD equal 10
So, D need not be true.

Answer: A, C

Cheers,
Brent