Question

Consider the statement |x - 3] < 2.5. a. What is the meaning of this statement? Select all that apply. - All values of whose distance from 2.5 is greater than 3. - All values of whose distance from 2.5 is less than 3. - All values of whose distance from 3 is greater than 2.5. - All values of whose distance from 3 is less than 2.5.

Answer 1

Answer: Choice D

All values of whose distance from 3 is less than 2.5

Reason:

x is some unknown number on the number line.

|x-3| is the number line distance from x to 3.

|x-3| < 2.5 means we make that distance less than 2.5 units.

As a bit of extra information, that inequality solves to 0.5 < x < 5.5 meaning that x is between 0.5 and 5.5 excluding both endpoints.