SOLVING INEQUALITIES WORKSHEET

Solving Inequalities Worksheet :

Worksheet given in this section is much useful to the students who would like to practice problems solving inequalities. 

Before look at the worksheet, if you would like to know the basic stuff about solving inequalities, 

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Solving Inequalities Worksheet - Problems

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

Solving Inequalities Worksheet - Solutions

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

After having gone through the stuff given above, we hope that the students would have understood, how to solve inequalities. 

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