PSAT Math Multiple-Choice Question 22: Answer and Explanation

Question: 22

10(3x + a) - a(4x + 2) = 2a(x + 4)

If the equation above has infinitely many solutions for x, what is the value of a?

• A. 5
• B. 4
• C. 3
• D. 1

Correct Answer: A

Explanation:

A

The question asks for the value of a. Since the equation has infinitely many solutions for x, any value of x can be used to find the value of a. Plug in an easy number for x. If x = 1, the equation becomes 10(3(1) + a) - a(4(1) + 2) = 2a(1 + 4). Distribute the numbers before the parentheses to get 30 + 10a -4a - 2a = 2a + 8a. Combine like terms to get 30 + 4a = 10a. Subtract 4a from both sides to get 30 = 6a. Divide both sides by 6 to get a = 5. The correct answer is (A).