Which of the following is the solution to | x-12 |< 15?
a. x< 27
b. x< 27 or x> -3
c. x< 27 and x< -3
d. x< 27 and x> -3

C

Step-by-step explanation:

Case 1

x-12 < 15

+12 each side

x < 27

Check case 1

|27-12| = 15

|15| = 15

15 = 15

So x<27 is correct but we still have to evaluate for the possibility of case 2

Case 2

x-12 < -15

+12 each side

x < -3

Check case 2

|-3-12| = 15

|-15| = 15

15 = 15

So -3 is also valid

Therefore your answer would be

C. x<27 and x<-3

x < 27 and x > -3

Step-by-step explanation: