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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