Bunuel wrote:

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. \(7a = 3b - 2\)

Let’s analyze each answer choice.

A. 49a^2 + 4 = 9b^2

If we subtract 4 from both sides of the equation, we have 49a^2 = 9b^2 - 4. This is equivalent.

B. 98a^2 = 18b^2 - 8

If we divide both sides of the equation by 2, we have 49a^2 = 9b^2 - 4. This is equivalent.

C. 49a^2 = (3b - 2)(3b + 2)

If we expand the right-hand side of the equation, we have 49a^2 = 9b^2 - 4. This is equivalent.

D. a^2 = (9b^2 - 4)/7^2

If we divide both sides of the equation by 7^2 = 49, we have 49a^2 = 9b^2 - 4. This is equivalent.

Thus, the correct answer must be E. However, let’s analyze it anyway.

E. 7a = 3b - 2

If we square both sides of the equation, we have (7a)^2 = (3b - 2)^2, or 49a^2 = 9b^2 - 12b + 4, which is not the same is 49a^2 = 9b^2 - 4.

Answer: E

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Jeffery Miller

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