SAT/ACT problem of the week, January 26, 2017 solution

Hint for process of elimination: Taking test values such as $latex a=3 $ and $latex b=5 $ and carefully using order of operations will help you eliminate most or all answers. If your own choice of values of $latex a $ and $latex b $ do not eliminate all choices, making a second choice (or in very extreme cases even a third choice) will finish off all remaining incorrect answers.

Another hint is, variables are never being multiplied with other variables, this eliminates choices D and E. Also, there is nothing in the original expression which can combine with and eliminate the number 2 from the expression. This eliminates choices A and C, leaving you with the correct answer, B.

Read on for a full solution.

Answer: B

Solution: You need to know that a negative sign can be distributed over parentheses because $latex -(a + b) = -1 \cdot (a+b) $. You also need to know that the product of a positive number and a negative number is negative, and the product of two negative numbers is positive. Use that to justify the following algebra:

$latex 5a+3b-(5b-2) = 5a+3b-5b+2 = 5a-2b+2 $, which is choice B.

Work it out! Make sure you get the same answer.

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