Question which-

2.4 Equivalent Expressions - Simplifying polynomials
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open parenthesis, one-half x, plus 3, close parenthesis, minus, open parenthesis, two-thirds x, minus 5, close parenthesis

Which of the following is equivalent to the expression above?

A.
negative one sixth x, plus 8
B.
negative one sixth x, minus 2
C.
negative one-third x squared, plus one-half x, plus 15
D.
negative one-third x squared, minus nine halves x, minus 15

Which of the following is equivalent to the expression above?

Hard-difficulty · SAT Math · Equivalent Expressions — Simplifying polynomials. Read the question above, select your answer, and check the full explanation below to understand exactly why the correct choice works.

Answer explanation

Choice A is correct. By distributing the minus sign through the expression two thirds x minus 5, the given expression can be rewritten as open parenthesis, one half x plus 3, close parenthesis, minus two thirds x, plus 5, which is equivalent to one half x, minus two thirds x, plus 3, plus 5. Combining like terms gives open parenthesis, one half minus two thirds, close parenthesis, times x, plus, open parenthesis, 3 plus 5, close parenthesis, or negative one sixth x plus 8.

Choice B is incorrect and may be the result of failing to distribute the minus sign appropriately through the second term and simplifying the expression one half x, plus 3, minus two thirds x, minus 5. Choice C is incorrect and may be the result of multiplying the expressions one half x plus 3 and negative two thirds x plus 5. Choice D is incorrect and may be the result of multiplying the expressions one half x plus 3 and negative two thirds x minus 5.