SOLVING INEQUALITIES WORKSHEET
Problem 1 :
Solve the following inequality :
x - 5 < 4
Problem 2 :
Solve the following inequality :
-x + 2 > 7
Problem 3 :
Solve the following inequality :
5x - 4 ≥ 4x + 6
Problem 4 :
Solve the following inequality :
4z + 8 ≤ 12
Problem 5 :
Solve the following inequality :
-m + 3 ≥ -4m + 6
Problem 6 :
Solve the following inequality :
-x + 2 > 7
Problem 7 :
Solve the following inequality :
2 > 3x - 10
Problem 8 :
Solve the following inequality :
16 - 2x ≤ 28
Detailed Answer Key
Problem 1 :
Solve the following inequality :
x - 5 < 4
Solution :
Solve for x :
x - 5 < 4
Add 5 to each side.
x < 9
Problem 2 :
Solve the following inequality :
-x + 2 > 7
Solution :
Solve for x :
-x + 2 > 7
Subtract 2 from each side.
-x > 5
Multiply each side by -1.
x < -5
Problem 3 :
Solve the following inequality :
5x - 4 ≥ 4x + 6
Solution :
Solve for x :
5x - 4 ≥ 4x + 6
Subtract 4x from each side.
x - 4 ≥ 6
Add 4 to each side.
x ≥ 10
Problem 4 :
Solve the following inequality :
4z + 8 ≤ 12
Solution :
Solve for z :
4z + 8 ≤ 12
Subtract 8 from each side.
4z ≤ 4
Divide each side by 4.
z ≤ 1
Problem 5 :
Solve the following inequality :
-m + 3 ≥ -4m + 6
Solution :
Solve for m :
-m + 3 ≥ -4m + 6
Add 4m to each side.
3m + 3 ≥ 6
Subtract 3 from each side.
3m ≥ 3
Divide each side by 3.
m ≥ 1
Problem 6 :
Solve the following inequality :
-x + 2 > 7
Solution :
Solve for x :
-x + 2 ≥ 7
Subtract 2 from each side.
-x > 5
Multiply each side by -1.
x < -5
Problem 7 :
Solve the following inequality :
2 > 3x - 10
Solution :
Solve for x :
2 > 3x - 10
Add 10 to each side.
12 > 3x
Divide each side by 3.
4 > x
Interchange the quantities on the left and right side.
x < 4
Problem 8 :
Solve the following inequality :
16 - 2x ≤ 28
Solution :
Solve for x :
16 - 2x ≤ 28
Subtract 16 from each side.
-2x ≤ 12
Divide each side by -2.
x ≥ -6
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