ExplanationIf a range of values for a can be found, then the range of values for \(a^2\) can be found.

Start by testing the end values of b, –3 and 1.

Plug in –3 for b in the first given inequality then solve for a.

You find that –4 < a < 7. If b = 1, 0 < a <11; b could be any integer in the range –3 ≤ b ≤ 1, this means –4 < a < 11 overall.

Remember to take the last step, though!

The question is looking for the range of \(a^2\), not a; \(a^2\) is always positive (i.e., \(0 < a^2\)).

Because a < 11, \(a^2 < 121\).

This means \(0 < a^2 < 121\); the answer is choice (D).

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Sandy

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