Question

The equation
24x2+25x−47/ax−2
=−8x−3−53/ax−2
is true for all values of x≠
2/a
, where a is a constant.

What is the value of a?

A) -16
B) -3
C) 3
D) 16

Answer 1

$- \: 3 \: \: \: is \: \: \: your \: \: \: answer$

Step-by-step explanation:

There are two ways to solve this question. The faster way is to multiply each side of the given equation by ax−2 (soyou can get rid of the fraction). When you multiply each side by ax−2, you should have:

$➠ \: 24 {x}^{2} \: +25x \: − \: 47= \: (−8x−3) \: (ax−2)−53$

You should then multiply (−8x−3) and (ax−2) using FOIL.

$➠ \: 24 {x}^{2} \: + \: 25x−47 \: = \: −8a {x}^{2} \: − \: 3ax \: + \: 16x \: + \: 6−53$

Then, reduce on the right side of the equation.

$➠24 {x}^{2} \: + \: 25x \: − \: 47 \: = \: −8a {x}^{2} − \: 3ax \: + \: 16x \: − \: 47$

Since the coefficients of the x² - term have to be equal on both sides of the equation, − 8a = 24, or a = − 3.

The other option which is longer and more tedious is to attempt to plug in all of the answer choices for a and see which answer choice makes both sides of the equation equal. Again, this is the longer option, and I do not recommend it for the actual SAT as it will waste too much time.

The final answer is B.