WORD PROBLEM: SUBTRACTING QUANTITY

Question

Betsy is asked by her instructor to subtract the quantity (−𝑎 + 5𝑏 − 9) from the quantity (2𝑎 − 3𝑏 − 2) and believes that the correct answer is 3𝑎 + 8𝑏 − 11. Is she correct? If not, then what is wrong with her answer?

Answer 1

Betsy is incorrect! Subtracting quantities can be very tricky and you have to pay special attention to the positive and negatives signs!

First set it up like this: (2a - 3b - 2) - (-a + 5b - 9)

Now distribute the negative into the second set of parentheses: 2a - 3b -2 + a - 5b +9

Notice that the -a became positive (because the minus sign turns another minus sign positive), the + 5b became negative (a minues turns a plus to a minus), and the -9 became +9 (again, two minus signs make a positive). Everything in the first parentheses stays the same.

Now, we can add like terms: 2a + a - 3b - 5b -2 + 9 = 3z - 8b + 7