Solutions of inequality practice

Answer 1

1. Solve the inequality: 2x + 5 < 15
Subtract 5 from both sides: 2x < 10
Divide by 2: x < 5

2. Solve the inequality: 3(x - 2) ≥ 9
Distribute the 3: 3x - 6 ≥ 9
Add 6 to both sides: 3x ≥ 15
Divide by 3: x ≥ 5

3. Solve the compound inequality: -2 < 3x + 4 ≤ 10
Subtract 4 from all parts of the inequality: -6 < 3x ≤ 6
Divide by 3: -2 < x ≤ 2

4. Solve the inequality: 4 - 2x > 8
Subtract 4 from both sides: -2x > 4
Divide by -2 (note that the inequality sign flips): x < -2

5. Solve the inequality: 7x + 3 ≥ 10x - 15
Subtract 7x from both sides: 3 ≥ 3x - 15
Add 15 to both sides: 18 ≥ 3x
Divide by 3: 6 ≥ x or x ≤ 6