SOLVING INEQUALITIES WITH VARIABLES ON BOTH SIDES WORKSHEET

Solving Inequalities with Variables on Both Sides Worksheet :

Worksheet given in this section will be much useful for the students who would like to practice solving inequalities with variables on both sides. 

Solving Inequalities with Variables on Both Sides Worksheet - Questions

Question 1 :

Solve the following linear inequality 

3x - 7 > x + 1

Question 2 :

Solve the following linear inequality 

x + 5 > 4x - 10

Question 3 :

Solve the following linear inequality 

3x + 9 ≥ -x + 19

Question 4 :

Solve the following linear inequality 

3x + 17 ≤ 2(1 - x)

Solving Inequalities with Variables on Both Sides Worksheet - Answers

Question 1 :

Solve the following linear inequality 

3x - 7 > x + 1

Answer :

3x - 7 > x + 1

Subtract x on both sides

3x - x - 7 > x - x + 1

2x - 7 > 1

Add 7 on both sides

2x - 7 + 7 > 1 + 7

2x > 8

Divide by 2 on both sides

2x/2 > 8/2

x > 4

Hence the solution set of the given inequality is (4, ∞)

Question 2 :

Solve the following linear inequality 

x + 5 > 4x - 10

Answer :

x + 5 > 4x - 10

Subtract 4x on both sides

x - 4x + 5 > 4x - 4x - 10

-3x + 5 > -10

Subtract 5 on both sides

-3x + 5 - 5 > -10 - 5

-3x > -15

Divide by -3 on both sides

x < 5

Hence the solution set of the given inequality is (-∞, 5)

Question 3 :

Solve the following linear inequality 

3x + 9 ≥ -x + 19

Answer :

3x + 9 ≥ -x + 19

Add x on both sides

3x + x + 9 ≥ -x + x + 19

4x + 9  ≥  19

Subtract 9 on both sudes

4x + 9 - 9  ≥ 19 - 9

4x  ≥ 10

Divide by 4 on both sides

x  ≥ 10/4

x  ≥ 5/2

Hence the solution set of the given inequality is  [5/2, ∞)

Since we have grater than or equal sign, we have used closed parentheses to write 5/2.

Question 4 :

Solve the following linear inequality 

3x + 17 ≤ 2(1 - x)

Answer :

3x + 17 ≤ 2(1 - x)

By using distributive property on the right side, we get

3x + 17 ≤ 2 - 2x

Add 2x on both sides

3x + 2x + 17 ≤ 2 - 2x + 2x

5x + 17 ≤ 2

Subtract 17 on both sides

5x + 17 - 17 ≤ 2 - 17

5x ≤ -15

Divide by 5 on both sides

x ≤ -15/5

x ≤ -3

Hence the solution set of the given inequality is  (-∞, -3]

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

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