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**1. Homework Statement**

if |x-3| < ε/7 and 0 < x ≤ 7 prove that |x^2 - 9| < ε

**2. Homework Equations**

**3. The Attempt at a Solution**

So ths is what I did so far.

|x+3|*|x-3| < ε (factored out the |x^2 - 9|)

|x+3|*|x-3| < |x+3|* ε/7 < ε (used the fact that |x-3| < ε/7)

|x+3|* ε/7 *7 < ε*7|x-3| < ε/7*7 (multiplied both sides of the inequality by 7)

I suck at epsilon delta proofs and have no idea where to go from here.