Question

Which compound sentence is the equivalent of |x - 5| = 4?
A. x - 5 > 4 or x - 5 < -4
B. -4 < x - 5 < 4
C. -8 < 2x + 3 < 8
D. x - 5 = 4 or x - 5 = -4
E. 2x + 3 > 8 or 2x + 3 < -8

Answer 1

It can only be D because an equality wouldn't have greater than or less than signs in it.

Answer 2

D. x - 5 = 4 or x - 5 = -4
When you take the absolute value of a number, you always end up with a positive number (or zero). Whether the input was positive or negative (or zero), the output is always positive (or zero). For instance, | 3 | = 3, and | –3 | = 3 also.
http://www.purplemath.com/modules/solveabs.htm