PSAT Math Multiple-Choice Question 557: Answer and Explanation

Question: 557

For the equation 3 + 4x - 2 = k + 6x - 2x, what does the constant k need to equal in order for there to be multiple solutions for x

• A. 1
• B. 2
• C. 3
• D. 4

Correct Answer: A

Explanation:

(A) Before proceeding too far, simplify the equation by grouping like terms:

3 + 4x - 2 = k + 6x - 2x

1 + 4x = k + 4x

So if k = 1, both sides of the equations are equivalent to one another. The equation reduces to x = x, which has an infinite number of solutions.