Question

Question 2

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

What is the value of a?

A) -16
B) -3
C) 3
D) 16​

Answer 1

Step-by-step explanation:

⭐ANSWER EXPLANATION:

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.

Answer 2

${\boxed{\mathfrak{ Answer}}}$

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

What is the value of a?

A) -16

B) -3

C) 3

D) 16

____________________________

${\boxed{\mathfrak{{\pink{B}{\blue{y}:{\red{E}{\blue{m}{\green{p}{\blue{t}{\purple{y}{\red{z}{\pink{z}}}}}}}}}}}}}$