ACT Question on Absolute Value

Question

What is the value of the expression below?⎪⎪−8 + 4⎪ − ⎪3 − 9⎪⎪

A. −18

B. 0−2

C. 00

D. 02

E. 18

Answer 1

Things to know: absolute value symbols act like parentheses. Also, PEMDAS is still a thing. The most common mistake is to just turn EVERYTHING into a plus sign when it's inside absolute value symbols. No. Don't do that. Actually do the indicated arithmetic until you're left with ONE number inside the absolute value symbols, THEN make it positive. So let's do it...

⎪⎪−8 + 4⎪ − ⎪3 − 9⎪⎪... do the subtraction on the inner thing things.

⎪ ⎪−4⎪  −  ⎪−6⎪ ⎪... now it's only ONE number inside each abs val, make em positive.

⎪ 4  −  6 ⎪... now do the same thing.

⎪ −2 ⎪... now apply the outer abs val, and the answer is............

2

Answer 2

Starting from inside the abs value functions and working our way out:

|⎪−8 + 4⎪ − ⎪3 − 9⎪⎪=| |-4|-|-6||=|4-6| =|-2|=2 so the answer is D

Jim