Question

I really need help with this. SAT question‼️

The equation
24
x
2
+
25
x
−
47
a
x
−
2
=
−
8
x
−
3
−
53
a
x
−
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

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

24x2+25x−47=(−8x−3)(ax−2)−53

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

24x2+25x−47=−8ax2−3ax+16x+6−53

Then, reduce on the right side of the equation

24x2+25x−47=−8ax2−3ax+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.

Step-by-step explanation: