Inequalities

Solve the following inequality:

x + 2 > 12

• subtract 2 from both sides and your answer is

  x = 10

• subtract 2 from both sides and your answer is

  x > 10

• subtract 2 from both sides and your answer is

  X < 10

Solve 5x > 10

• divide by 5 on both sides and your answer is

  x = 2

• divide by 5 on both sides and your answer is

  x < 2

• divide by 5 on both sides and your answer is

  x > 2

Solve 3x + 2 > 8

• subtract 2 from both sides and your answer is

  x > 6

• subtract 2 from both sides and your answer is

  x = 6

• subtract 2 from both sides and then divide by 3 on both sides and your answer is

  x > 2

Solve the inequality

3x - 7 < 5

• x < 4

• x < -2

• x = 4

Try some:

-2x ≤ 4

• divide by -2 o both sided and your answer will be

  x = -2

• divide by -2 on both sides and you will switch the direction of the inequality since you are dividing by a negative and your answer will be

  x ≥ -2

• divide by -2 on both sides and your answer will be

  x ≤ -2

- 3x < -12

• divide both sides by -3 and your answer is

  x < 4

• x = 4

• divide both sides by -3 and your answer is

  x > 4

  because you divided by a negative and had to flip the inequality symbol

Example

x ≥ 3

−2

• multiply both sides by -2 and your answer will be

  x ≤ -6

  because you multiplied by a negative you must switch the inequality

• multiply both sides by -2 and your answer will be

  x ≥ -6

• divide both sides by -2 and you get

  x ≥ -2/3

Greater than or equal to

• <

• >

• ≤

• ≥

Greater than

• <

• >

• ≤

• ≥

Less than or equal to

• <

• >

• ≤

• ≥