Question

Solve the compound inequality |3x-9|≤15 and |2x-3|≥5. Give answer in interval notation.

Answer 1

Explanation:

|3x-9|≤15

-15≤3x-9≤15

-15+9≤3x≤15+9

-6≤3x≤24

-2≤x≤8

x∈[-2,8]

|2x-3|≥5

2x-3≤-5

2x≤-2

x≤-1

and

2x-3≥5

2x≥8

x≥4

solution is x∈[-2,-1]∪[4,8]