1. Final Exam Review of Inequalities
5/31/2013
Final Exam Review of Inequalities

2. Translate the following statements into inequalities.
Six less than double a number is less than 18.
2x – 6 < 18
Eight more than five times a number is greater than or equal to 48.
8 + 5x ≥ 48

3. 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!

4. Solve and graph the following inequality.
3x + 8 > - 4
3x > -12
x > -4
Remember! An open circle is used to graph > and <.
Check: @ x = -3
3x + 8 > -4
3(-3) + 8 > -4
> -4
-1 > -4

5. Solve and graph the following inequality.
-7x - 3 ≥ 11
-7x ≥ 14
x ≤ -2
A closed circle is used to graph ≥ and ≤.
Check: @ x = -4
-7x - 3 ≥ 11
-7(-4) – 3 ≥ 11
≥ 11
25 ≥ 11
Important! Change the direction of the inequality sign if you multiply or divide both sides by a negative.

6. Solve and graph the following inequality.
- 9 < -3(2x – 5)
- 9 < -6x + 15
-24 < -6x
4 > x
x < 4
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.