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Question

Solving Inequalities with Variables on Both Sides: Match the following inequalities.

1. 2x+1>3x

2. x+12<-5x

3. 4x-8≥2x+6

4. -2x+6≤4x+18

5. -10x+50≤-20-20

6. 8x+24>16x-48

7. -3x-5≤2x+10

8. 4x+20<12x-60

9. 2x-7≤-x+5

10. -x+6≥-2x+3

Answer 1

1). 2x + 1 > 3x.

2x - 3x > - 1

-x >- 1

x < 1.

The solution set is { x | x < 1}.

2). x + 12  < - 5x.

x + 5x < - 12

6x < - 12

x < - 12 / 6

x < - 2.

The solution set is { x | x < - 2}.

3). 4x - 8 ≥ 2x + 6.

4x - 2x ≥ 6 + 8

2x ≥ 14

x ≥ 14 / 2

x ≥ 7.

The solution set is { x | x ≥ 7}.

4). - 2x + 6 ≤ 4x + 18.

- 2x - 4x ≤ 18 - 6

- 6x ≤ 12

x ≥ - 12 / 6

x ≥ - 2.

The solution set is { x | x ≥ - 2}.

5). - 10x + 50 ≤ - 20 - 20.

- 10x + 50 ≤ - 40

- 10x ≤ - 40 - 50

- 10x ≤ - 90

x ≥ - 90 / - 10

x ≥ 9.

The solution set is { x | x ≥ 9}.

6). 8x + 24 > 16x - 48.

8x - 16x > - 48 - 24

- 8x > - 72

x < 72 / 8

x < 9.

The solution set is { x | x < 9}.

7). - 3x - 5 ≤ 2x + 10.

- 3x - 2x ≤  10 + 5

- 5x ≤  15

x ≥ - 3.

The solution set is { x | x ≥ - 3}.

8). 4x + 20 < 12x - 60.

4x - 12x < - 60 - 20

- 8x < - 80

x > 80 / 8

x > 10.

The solution set is { x | x > 10}.

9). 2x - 7 ≤ - x + 5.

2x + x ≤ 5 + 7

3x ≤ 12

x ≤ 12 / 3

x ≤ 4.

The solution set is { x | x ≤ 4}.

10). - x + 6 ≥ - 2x + 3.

- x + 2x ≥ 3 - 6

x ≥ - 3.

The solution set is { x | x ≥ - 3}.

Observe the above inequalities, the inequalities 7 & 10 have same solution sets.