2_6classnotes

2.6 Solving Inequalities
Homework: EOO 5 – 85

· Graphing inequalities on a number line.

Since all the solutions of an inequality cannot be listed, a graph is drawn to show where the solutions lie on the number line.
A closed circle is used to indicate that an endpoint is a solution and is used for .
An open circle is used to indicate that an endpoint is not a solution and is used for < or >.

Example: Graph each of the following on a separate number line.

· Using Interval Notation to write solutions of inequalities.
Intervals of numbers are enclosed in parentheses, brackets, or a combination of the two as follows:
An interval must read from the smaller (left) to the larger number (right).
For a bracket will be used beside the endpoint.
For < or > a parenthesis will be used beside the endpoint.
A parenthesis is used beside .

Write Intervals for the following inequalities.

Examples:

· Set-Builder Notation
Braces are used to enclose a set. The variable is written first, followed by a vertical line (which is read such that), followed by the inequality.
Example:

Example:
x < 9

· Solving Inequalities:
The process is the same as when solving equations except:
The inequality symbol reverses when you divide or multiply by a negative number.
The inequality symbol reverses when you change the order of the statement.

Examples:
-6 < -3

6 > 3 Divided both sides by –1.

-5x > 10
x < -2 Divided both sides by –5.

4 > x
x < 4 Changed the order of the statement.

· Examples of Inequalities to Solve.
Graph, Write Interval, and Write Set-Builder notation for each:

Graph will have a closed circle at 4, graph goes to the right of 4.
Interval is:

Set-Builder notation is:

Graph will have an open circle at –2, graph goes to the left of –2.
Interval is:

Set-Builder notation is:

· Describe each graph using interval notation and set-builder notation.
1. The graph has an open circle at 3 and graph is to the left of 3.
Interval:

Set-Builder:

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