There are two ways to solve this question. The faster way is to multiply each side of the given equation by
a
x
−
2
(so you can get rid of the fraction). When you multiply each side by
a
x
−
2
, you should have:
24
x
2
+
25
x
−
47
=
(
−
8
x
−
3
)
(
a
x
−
2
)
−
53
You should then multiply
(
−
8
x
−
3
)
and
(
a
x
−
2
)
using FOIL.
24
x
2
+
25
x
−
47
=
−
8
a
x
2
−
3
a
x
+
16
x
+
6
−
53
Then, reduce on the right side of the equation
24
x
2
+
25
x
−
47
=
−
8
a
x
2
−
3
a
x
+
16
x
−
47
Since the coefficients of the
x
2
-term have to be equal on both sides of the equation,
−
8
a
=
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.