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Question

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

11. 7-x<5+x

12. 19+x>-16+2x

13. 37-2x≤-33-x

14. 4x-16>x+2

15. 5x-100≤10x-200

16. 3x+6>9x-6

17. 2x+3>x-4

18. 60-4x≤16

19. 300+10x≥20x-600

20. -25x+50<75x-1150

Answer 1

11) 7- x  < 5 + x

- x  - x  < 5 -7

-2x  < -2

Multiply each side by negative 2 and flip the symbol.

x  > 1

Solution set {x |x  > 1}

12) 19 + x  > -16 + 2x

x  - 2x  > -16 -19

-x  > -35

Multiply each side by negative one and flip the symbol.

x  < 35

Solution set {x |x  < 35}

13) 37-2x  ≤ -33 -x

-2x  + x  ≤ - 33 - 37

-x  ≤ -70

Multiply each side by negative one and flip the symbol.

x  ≥ 70

Solution set {x |x  ≥ 70}

14) 4x  - 16 > x  + 2

4x  - x  > 16 + 2

3x  > 18

x  > 6

Solution set {x |x  > 6}

15) 5x  - 100 ≤ 10x  - 200

5x  - 10x  ≤ -200 + 100

-5x  ≤ -100

Divide each side by negative 5 and flip the symbol.

x  ≥ 20

Solution set {x |x  ≥ 20}

16) 3x  + 6 > 9x  - 6

3x  - 9x  > -6 -6

-6x  > -12

Divide each side by negative 6 and flip the symbol.

x  < 2

Solution set {x |x  < 2}

17) 2x  + 3 > x  - 4

2x  - x  > -4 -3

x  > -7

Solution set {x |x  > -7}

18) 60 - 4x  ≤ 16

-4x  ≤ 16 - 60

-4x  ≤ -44

Divide each side by negative 4 and flip the symbol.

x  ≥ 11

Solution set {x |x  ≥ 11}

19) 300 + 10x  ≥ 20x  - 600

10x  - 20x  ≥ - 600 - 300

-10x  ≥ -900

Divide each side by negative 10 and flip the symbol.

x  ≤ 90

Solution set {x |x  ≤ 90}

20) -25x  + 50 < 75x  - 1150

-25x  -75x  < -1150 - 50

-100x  < -1200

Divide each side by negative 100 and flip the symbol.

x  > 12

Solution set {x |x  > 12}.