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

Hint for process of elimination: Taking test values such as $a=3$ and $b=5$ and carefully using order of operations will help you eliminate most or all answers. If your own choice of values of $a$ and $b$ 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.

Solution: You need to know that a negative sign can be distributed over parentheses because $-(a + b) = -1 \cdot (a+b)$. 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:
$5a+3b-(5b-2) = 5a+3b-5b+2 = 5a-2b+2$, which is choice B.