solve inequalities practice

Answer 1

1. Solve the inequality: 2x + 5 > 11

Subtract 5 from both sides:
2x > 6

Divide by 2 on both sides:
x > 3

Therefore, the solution is x > 3.

2. Solve the inequality: 3(2x - 1) ≤ 12

Expand the left side:
6x - 3 ≤ 12

Add 3 to both sides:
6x ≤ 15

Divide by 6 on both sides:
x ≤ 2.5

Therefore, the solution is x ≤ 2.5.

3. Solve the inequality: -4x + 7 < 15

Subtract 7 from both sides:
-4x < 8

Divide by -4 on both sides (remember to flip the inequality sign when dividing by a negative number):
x > -2

Therefore, the solution is x > -2.

4. Solve the inequality: 2x/3 - 4 > 2

Add 4 to both sides:
2x/3 > 6

Multiply by 3 on both sides:
2x > 18

Divide by 2 on both sides:
x > 9

Therefore, the solution is x > 9.

5. Solve the inequality: -2x + 5 ≤ 1

Subtract 5 from both sides:
-2x ≤ -4

Divide by -2 on both sides (remember to flip the inequality sign when dividing by a negative number):
x ≥ 2

Therefore, the solution is x ≥ 2.