If 3x4 - 2 = 7, what is the value of 3x - 8? | SAT Linear equations in one variable Question, Answer Explained

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Question bank / Linear equations in one variable

Math · AlgebraMedium

If $\frac{3x}{4} - 2 = 7$ , what is the value of $3x - 8$ ?

$12$

$22$

$28$

$36$

Show answer and explanation

Answer: C

Multiply both sides of the equation by $4$ : $3x - 8 = 28$ . This is exactly the expression the question asks for. Solving for $x$ also works: $\frac{3x}{4} = 9$ , so $x = 12$ and $3(12) - 8 = 28$ .

Choice B multiplies only the $\frac{3x}{4}$ term by $4$ , which gives $3x - 2 = 28$ instead of $3x - 8 = 28$ .

Why the other choices are wrong

A. 12 is the value of x, not the value of 3x - 8.
B. This multiplies only the 3x/4 term by 4 and leaves the -2 unchanged. Every term must be multiplied by 4.
D. 36 is the value of 3x. Subtract 8 to get 3x - 8.

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