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

So in order to find the value of a, we can start by simplifying the equation:

\[\frac{ 24x^2 + 25x - 47 }{ ax - 2 } = 7-8x - 3 - \frac{ 53 }{ ax -2 }\]

Now, we'll eliminate the fractions:

$$24x^2 + 25x - 47 = (-8x - 3)(ax - 2) - 53$$

Then we'll expand the right side of the equation by using foil and this will give youl:

$$24x^2 + 25x - 47 = -8ax^2 + 16x - 3ax + 6 - 53$$


Then we'll combine the like terms:

$$24x^2 + 25x - 47 = -8ax^2 + (16 - 3a)x - 47$$


FInally we'll equate the coefficients:

$$24 = -8a$$

$$a = \frac{24}{-8}$$

$$a = -3$$


FInally we'll verify with the x coefficients:

$$25 = 16 - 3a$$

$$25 = 16 - 3(-3)$$$$25 = 16 + 9$$

$$25 = 25$$


So your final answer is -3 (B)

Answer 2

the anwser is A good job

Answer 3

You're joking.

Answer 4

no dead Salsa

Answer 5

At least I tried :sob: