Question

How do you solve the compound inequality? 6 – x > 15 or 2x – 9 ≥ 3

Answer 1

x < -9 or x ≥ 6

Explanation:

6 – x > 15 or 2x – 9 ≥ 3

Solve each inequality

6-x > 15

Subtract 6 from each side

6-x-6 > 15-6

-x > 9

Multiply by -1 remembering to flip the inequality

x < -9

Then the other inequality

2x – 9 ≥ 3

Add 9 to each side

2x -9+9≥ 3 +9

2x≥ 12

Divide by 2

2x/2 ≥ 12/2

x ≥ 6

Put back together

x < -9 or x ≥ 6