Question

(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?

Answer 1

hi

Step-by-step explanation:

multiply both sides of the given equation by ax−2. 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.

so answer is -3

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