Question

Select the set of equations that would be used to solve the following absolute value equation: |x+6|=18

A. x-6=18 and x+6=18
B. x-6=18 and x-6=-18
C.x+6=18 and x+6=-18
D. x-6=18 and -x+6=-18

Answer 1

The answer is A. x-6=18 and x+6=18.

Answer 2

|x + 6| = 18

absolute value just tells you how many units a value is from 0 on a number line. |-1|, for example, is 1 unit away from the number line. |383| is 383 units away. with that being said, the answer to absolute value equations is set up like so:

x + 6 = 18
or
x + 6 = -18

so basically, the absolute value of (x + 6) is 18 units away from 0 on a number line, but it could be 18 units in the positive or negative direction, so you have to look for both by setting it to both -18 and 18. your answer is C.