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S95-28

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Math Expert
Joined: 02 Sep 2009
Posts: 43361

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16 Sep 2014, 00:50
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Difficulty:

25% (medium)

Question Stats:

91% (00:25) correct 9% (00:46) wrong based on 23 sessions

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Which of the following is NOT equivalent to $$49a^2 = 9b^2 - 4$$?

A. $$49a^2 + 4 = 9b^2$$
B. $$98a^2 = 18b^2 - 8$$
C. $$49a^2 = (3b - 2)(3b + 2)$$
D. $$a^2 = \frac{9b^2 - 4}{7^2}$$
E. $$7a = 3b - 2$$
[Reveal] Spoiler: OA

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Joined: 02 Sep 2009
Posts: 43361

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16 Sep 2014, 00:50
Official Solution:

Which of the following is NOT equivalent to $$49a^2 = 9b^2 - 4$$?

A. $$49a^2 + 4 = 9b^2$$
B. $$98a^2 = 18b^2 - 8$$
C. $$49a^2 = (3b - 2)(3b + 2)$$
D. $$a^2 = \frac{9b^2 - 4}{7^2}$$
E. $$7a = 3b - 2$$

Four of the answer choices are equivalent to $$49a^2 = 9b^2 - 4$$, and one is not. Equations are said to be equivalent when the equations have the same solution.

In this case, equivalent equations will have the same value for $$a$$ and $$b$$ as in the original equation. Let's compare our equation to each choice.

Choice A: $$49a^2 + 4 = 9b^2$$ is the same as the original equation if 4 is added to both sides. Eliminate A.

Choice B: $$98a^2 = 18b^2 - 8$$ is the same as the original equation if both sides are multiplied by 2. Eliminate B.

Choice C: $$49a^2 = (3b - 2)(3b + 2)$$ correctly factors the original equation. Eliminate C.

Choice D: $$a^2 = \frac{9b^2 - 4}{7^2}$$ is the same as the original equation if both sides are divided by $$7^2$$ or $$49$$. Eliminate D.

Choice E: $$7a = 3b - 2$$ incorrectly calculates the square root of $$9b^{2} - 4$$. The square root of the left side of the equation is correctly calculated. However, the square root of $$9b^{2} - 4$$ isn't $$3b - 2$$. We can verify this by squaring $$3b - 2$$. If we do, we get $$9b^{2} - 12b + 4$$, which is not equivalent to $$9b^{2} - 4$$.

Choice E, which is not equivalent, is thus correct.

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08 Dec 2017, 13:41
What is the square root of 9b^2 − 4, anyway?
Re: S95-28   [#permalink] 08 Dec 2017, 13:41
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