1. Chapter 1.5
Solving Inequalities

2. By the end of this lesson you will know how to:
What the Trichotomy Property is
How to use the basic properties to solve inequalities
How to show the solutions using set builder notation and interval notation

3. Trichotomy Property
For any two real numbers, a and b, exactly one of the following statements is true.
a<b a=b a>b
a≤b a=b a≥b
Adding the same number to, or subtracting the same number from, each side of an inequality does not change the truth of the inequality.

4. Multiplying or dividing within an inequality
Remember – when multiplying or dividing each side of an inequality by a positive number, nothing changes.
However, when multiplying or dividing each side by a negative number, the order of the inequality must be reversed.

5. Example #1
-8N ≥ 56
Because we have to divide both sides by negative 8 – we have to switch the inequality symbols.
N ≤ -7

6. Example #2
When you multiply or divide by a positive number – you do not have to switch the inequality symbol
2N < 36
N < 18

7. Notations Set Builder Notation
This is read as the set of all numbers x such that x is greater than 9

8. Interval Notations
The infinity symbols +∞ and -∞ are used to indicate that a set is unbounded in the positive or negative direction. To show that the endpoint is not included in the set, a parenthesis is used.
The solution set is (-∞, 5] and is graphed below.

9. Tonight’s Homework
Page 37
(15-37 Odd)