Question

Which of the values satisfy the following inequality

|x-7.5|≤ 17
Select all that apply.
A: x= 20
B: x= -10
C: x= -9
D: x= 27

Answer 1

A: x = 20

C: x = -9

Explanation:

You can solve the inequality and compare that with the offered choices, or you can try the choices in the inequality to see if it is true. Either approach works, and they take about the same effort.

Solving it:

Unfold it ...

-17 ≤ x -7.5 ≤ 17

Add 7.5 ...

-9.5 ≤ x ≤ 24.5

The numbers 20 and -9 are in this range: answer choices A and C.

_____

Trying the choices:

A: |20 -7.5| = 12.5 ≤ 17 . . . . this works

B: |-10 -7.5| = 17.5 . . . doesn't work

C: |-9 -7.5| = 16.5 ≤ 17 . . . . .this works

D: |27-7.5| = 19.5 . . . doesn't work

The choices that work are answer choices A and C.