Question

Solve the following inequality algebraically. 4|6 – 3x|+ 8 < 20 Absolute value inequalities

Answer 1

4|6 – 3x| + 8 < 20

8 is adding on the left, then it will subtract on the right

4|6 – 3x| < 20 - 8

4|6 – 3x| < 12

4 is multiplying on the left, then it will divide on the right

|6 – 3x| < 12/4

|6 – 3x| < 3

Now, we have two options:

6 - 3x < 3 or 6 - 3x > -3

-3x < 3 - 6 -3x > -3 - 6

-3x < -3 -3x > -9

x > (-3)/(-3) x < (-9)/(-3)

x > 1 x < 3

solution: 1 < x < 3