SAT Math Multiple Choice Question 656: Answer and Explanation

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Question: 656

11. The equation Images is true for all values of Images, where b is a constant. What is the value of b?

  • A. -12
  • B. -6
  • C. 4
  • D. 6

Correct Answer: B

Explanation:

B

Advanced Mathematics (rational equations) MEDIUM-HARD

The fact that the denominators are equal in both fractions suggests that multiplying both sides will simplify

Images

Multiply by

bx - 3: 12x2 + 6x - 23 = -2x(bx - 3) - 23

Distribute:

12x2 + 6x - 23 = -2bx2 + 6x - 23

Subtract 6x - 23:

12x2 = -2bx2

Divide by x2:

12 = -2b

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