Solutions of inequality practice test for math b6.23

Answer 1

1. Solve the inequality: 3x + 5 < 17

Subtract 5 from both sides:
3x < 12

Divide by 3:
x < 4

2. Solve the inequality: 2(6 - x) ≥ 10

Distribute the 2:
12 - 2x ≥ 10

Subtract 12 from both sides:
-2x ≥ -2

Divide by -2 (remember to flip the inequality sign when dividing by a negative):
x ≤ 1

3. Solve the inequality: 4(x - 3) > 8

Distribute the 4:
4x - 12 > 8

Add 12 to both sides:
4x > 20

Divide by 4:
x > 5

4. Solve the compound inequality: 2x + 5 < 15 and x - 3 ≥ 8

First inequality:
2x < 10
x < 5

Second inequality:
x ≥ 11

Therefore, the solution to the compound inequality is x < 5 or x ≥ 11.