m^2 < 9 means that -3 < m < 3. Combined with m > -1, we get that -1 < m < 3. Any m from this range must be greater than -3, hence A must be true.

Answer: A.
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The question tells us \(m^2 < 9\), which simplifies to \(-3 < m < 3\).

We are also told that \(m > -1\). Combining the two conditions we get, \(-1 < m < 3\).

Now the question asks, what must be true. Let's look at the answer choices one at a time.

(A) \(m > -3\) ---- Since \(m > -1\), this will always be true. We have our answer and can stop right here. But let's look at the other answer choices just to be certain.

(B) \(m > 1\) ---- Not necessary. \(m\) can be \(0\).

(C) \(m > 3\) ---- False. \(m\) can never be more than \(3\).

(D) \(m < 1\) ---- Not necessary. \(m\) can be \(1\).

(E) None of the above ---- False, as we have already seen A is true.

So, the answer is A.

Hope that helps.

How m > -3 satisfy the must be true criteria.

Consider m = +4 does it satisfy?
-1 < m < 3

Should be E) None of the above.
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The correct answer is A, not E. You misinterpreted the question. We are given that that -1 < m < 3. If -1 < m < 3, then it must be true that m is greater than -3.
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since m^2>9
-3<m<3

given that m>-1

from both of these inequalities

m must be m>-3

Answer is A

Since m>-1
Hence m>-3

Smash that A.
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Check other similar questions from Trickiest Inequality Questions Type: Confusing Ranges (part of our Special Questions Directory).
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For Beginners
if m^2<9
= m^2-9<0
=(m-3)(m+3)<0
:- The roots are +3 and -3
so the range is -3<x<3 As per the Wavvy line method( don't get carried away by this Jargon just search for the keyword wavvy ,it is an easy concept of quadratic Inequlaity which you should be aware of )
and the range is also m>-1
combined together the intersection region in the number line is
-1<x<3 is the final range

Now Analyze each answer choices

(A) m > -3
The Option A is always correct, because for any number in the range -1<x<3 is always greater than -3

(B) m>1
The Option B is not always correct for any number in the range -1<x <3, because there are also numbers less than 1 in the range

(C) m>3
The Option C is always wrong because we have the range as -1<x <3

(D) m<1
The Option D is not always correct for any number in the range -1<x <3, because there are also numbers greater than 1 in the range


(E) None of the above


Answer is A

m^2<9 -> -3<m<3
AND m>-1
Therefore -1<m<3
m>-3 is true to all m that satisfies the above inequality.

what if m= 4, it satisfies 1 but doesn't the equation in the question.

m cannot be 4 because m = 4 does not satisfy m^2 < 9. I suggest to check other similar questions from Trickiest Inequality Questions Type: Confusing Ranges (part of our Special Questions Directory).
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