In the equation 3(2x - 1) - 2(x + 4) = p(x - 5) + q, p and q... | SAT Linear equations in one variable Question, Answer Explained

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Math · AlgebraHard

In the equation $3(2x - 1) - 2(x + 4) = p(x - 5) + q$ , $p$ and $q$ are constants. If the equation has infinitely many solutions, what is the value of $q$ ?

$-31$

$-11$

$4$

$9$

Show answer and explanation

Answer: D

The left side simplifies to $6x - 3 - 2x - 8 = 4x - 11$ . The right side is $px - 5p + q$ . For infinitely many solutions, the coefficients of $x$ and the constants must match: $p = 4$ and $-5p + q = -11$ . So $-20 + q = -11$ and $q = 9$ .

Choice B sets $q$ equal to the constant $-11$ without accounting for the $-5p$ that the right side also contributes.

Why the other choices are wrong

A. This computes -11 - 20. Since -20 + q = -11, add 20 to -11 to get q.
B. This sets q equal to -11 and ignores the -5p that the right side also adds to the constant term.
C. 4 is the value of p, the coefficient of x, not q.

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