Bunuel wrote:
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.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,