Final Exam Reviewof Inequalities

Translate the following statements into inequalities.

1. Six less than double a number is less than 18.

2. Eight more than five times a number is greater than or equal to 48.

2x – 6 < 18

8 + 5x ≥ 48

Solving and Graphing Inequalities

• Solving inequalities is similar to solving equations, except….

– When you multiply or divide by a negative number, you have to change the direction of the inequality sign!

3. Solve and graph the following inequality.

3x + 8 > - 4 - 8 - 8

3x > -123 3 x > -4

-6 -5 -4 -3 -2

Check: @ x = -3

3x + 8 > -4

3(-3) + 8 > -4

-9 + 8 > -4

-1 > -4

Remember! An open circle is used to graph > and <.

4. Solve and graph the following inequality.

-7x - 3 ≥ 11 + 3 + 3

-7x ≥ 14-7 -7 x ≤ -2

-4 -3 -2 -1 0

Check: @ x = -4

-7x - 3 ≥ 11

-7(-4) – 3 ≥ 11

28 - 3 ≥ 11

25 ≥ 11

A closed circle is used to graph ≥ and ≤.

Important! Change the direction of the inequality sign if you multiply or

divide both sides by a negative.

5. Solve and graph the following inequality.

- 9 < -3(2x – 5) - 9 < -6x + 15-15 - 15 -24 < -6x -6 -6 4 > x x < 4

2 3 4 5 6

Check: @ x = 3

-9 < -3(2x – 5)

-9 < -3(2*3 – 5)

-9 < -3(6 - 5)

-9 < -3(1)

-9 < -3

The direction of the inequality sign changes since you divide by -6.