# 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

3x - 7 > x + 1

Subtract x on both sides

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

2x - 7 > 1

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

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

3x + 9 ≥ -x + 19

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

≥ 10/4

≥ 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)

3x + 17 ≤ 2(1 - x)

By using distributive property on the right side, we get

3x + 17 ≤ 2 - 2x

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

≤ -15/5

≤ -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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