SAT Linear equations in one variable Practice Question 17 (Hard)

Question bank / Linear equations in one variable

Math · AlgebraHard

In the equation $a(3x - 2) + 4 = 9x + b$ , $a$ and $b$ are constants. If the equation has infinitely many solutions, what is the value of $b$ ?

$-10$

$-2$

$2$

$4$

Show answer and explanation

Answer: B

Distribute: $3ax - 2a + 4 = 9x + b$ . For infinitely many solutions, the $x$ -coefficients must match, so $3a = 9$ and $a = 3$ . The constants must also match: $b = -2(3) + 4 = -2$ .

Choice C comes from a sign error, treating $-2a$ as $+2a$ and subtracting 4.

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