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

Question

Tough and Tricky questions: Algebra.

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

Kudos for a correct  solution .

DangerPenguin · Answer

I chose to put everything on one side of the equal sign.

49a^2 - 9b^2 - 4 = 0

Answer A: move everything to one side to get 49^2 - 9b^2 - 4 = 0, not equivalent

Answer A!

LighthousePrep · Answer

I tried to look for the common traps people face when they simplify equations. My attention went to choice E.

The reason is because it tries to simplify by square root-ing the equation, but the square root of  9b^2 - 4  does not equal  3b - 2 . It factors to  (3b+2)(3b-2) .

Therefore I know it is not equivalent to the equation in the question stem.

If I really wanted to validate that the other choices are in fact wrong, most of them require very simple algebraic operations to prove which can be done without pen and paper even.

A) Just add +4 to both sides.
B) Multiply both sides by 2.
C) Factor the right side of the equation. (This is what answer choice E tries to trap with.)
D) Divide both sides by 49,

PareshGmat · Answer

Answer = E

Original Equation

49a^2 = 9b^2 - 4

Option A, B, C, D are same as the original equation.... adjusting terms of LHS/RHS, multiply by 2 etc...

Option E

Square root the original equation

7a = \sqrt{9b^2 - 4} = \sqrt{(3b+2)(3b-2)}  .... This only far the equation can go

devmillenium2k · Answer

We just need to adjust equation as per the options and verify.

49a^2 = 9b^2 - 4 => 49a^2 + 4 = 9b^2 ----> Option a

Multiply by 2,
98a^2 = 18b^2 - 8 ----> Option b

49a^2 = 9b^2 - 4 => 49a^2 = (3b + 2)(3b - 2) ---> option c

a^2 = 9b^2 - 4 / 49 => a^2 = 9b^2 - 4 /7^2 ---- > option d

Take square root on both the sides
7a =  \sqrt{9b^2 - 4}  =  \sqrt{(3b+2)(3b-2)}  => This is not equal to 7a = 3b - 2

Hence answer is E.

Bunuel · Answer

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.

Answer: E.

Bunuel · Answer

Similar question from OG13: which-of-the-following-equations-is-not-equivalent-to-10y-138730.html

JeffTargetTestPrep · Answer

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

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

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