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?
Answers
Answer:
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 16
Answer:
Given,
ax−2
24x
2
+25x−47
=−8x−3−
ax−2
53
⇒
ax−2
24x
2
+25x−47
=
ax−2
(−8x−3)(ax−2)−53
⇒24x
2
+25x−47=(−8x−3)(ax−2)−53
⇒24x
2
+25x−47=−8ax
2
+16x−3ax+6−53
⇒24x
2
+25x−47=−8ax
2
+16x−3ax−47
⇒24x
2
+25x=−8ax
2
+(16−3a)x
⇒24=−8a
⇒a=−3