1. < < > > Inequalities
Sections and 10-6
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Inequalities

2. Examples of Inequalities
You must be at least 18 years old to vote. a > 18
The speed limit is 55 mph. s < 55
The package weight must be less than 80 pounds. w < 80
The president of the United States must be at least
35 years old. a > 35

3. Synonyms to Inequality
<
Less than or =
No more than
Up to
Is at most
<
Less than
Below
Under
Fewer than
>
Greater than
More than
Higher than
Over
Exceeds
>
Greater than or =
At least
A minimum of
Is no less than
Is at least

4. Detetrmine the Truth of an Inequality
State whether each inequality is true or false:
a + 2 > 8, a = 5
10 < 7 – x, x = -3
n – 6 < 15, n = 18
-3p > 24, p = 8
-2 > 5y – 7, y = 1

5. True or False ? x – 4 < 6, x = 0 3x > 4, x = 1 n > 5, n = 12
You try these
x – 4 < 6, x = 0
3x > 4, x = 1
n > 5, n = 12 4

6. Graph Inequality on a Number Line
n < 3 | | | | | | | | | | | | | | | | x > - 4

7. Your Turn: Graph These n > 3 x < 5 x < 1 n > - 1
b < - 4

9. Solving Inequalities by Adding or Subtracting
Same rules as for solving equations. If x – 2 = 3, add 2 to both sides, x = 5 If x – 2 > 5, add 2 to both sides, x > 5 If – 4 > a + 7, subtract 7 from both sides, - 11 > a or a > - 11

10. Your Turn: Solve These
A1) a + 3 > 12 22) 2 > p – 5 N3) n + ½ > 4 Y4) y - ⅓ < 5

11. Ticket Out the Door
South American manatees can weigh up to 1300 pounds. If one of the manatees weighs 968 pounds, up to how much weight might this manatee gain? Using w to represent the weight gained, write an inequality and solve it.