Which expression is equivalent to 5(x - 2) - 3(2x + 1)? | SAT Equivalent expressions Question, Answer Explained

Math · Advanced MathEasy

Which expression is equivalent to $5(x - 2) - 3(2x + 1)$ ?

$-x - 13$

$-x - 11$

$-x - 7$

$11x - 13$

Show answer and explanation

Answer: A

Distribute: $5x - 10 - 6x - 3$ . Combine like terms: $(5x - 6x) + (-10 - 3) = -x - 13$ .

Choice C treats $-3 \cdot 1$ as $+3$ ; distributing $-3$ gives $-6x - 3$ .

Why the other choices are wrong

B. This multiplies only the 2x by 3, leaving the constant as -1 instead of -3.
C. This treats -3 times 1 as +3. Distributing -3 gives -6x - 3.
D. This adds 6x instead of subtracting it. The -3 changes the sign of 2x as well.

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