INSTRUCTORS Carleen Eaton Grant Fraser

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### Solving Inequalities

• If both sides of an inequality are increased or decreased by the same number, or multiplied or divided by the same positive number, the resulting inequality is equivalent to the original one and has the same solutions.

• If both sides of an inequality are multiplied or divided by the same negative number, the direction of the resulting inequality must be reversed. The new inequality is equivalent to the original one and has the same solutions.

• Use set builder notation to describe the solution set of an inequality.

• The solutions to these inequalities can also be shown by shading the solution set on a number line. Endpoints should be drawn as solid dots if they are part of the solution set, and open circles otherwise.

### Solving Inequalities

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

• Intro 0:00
• Properties of Inequality 0:07
• Subtraction Property
• Example
• Multiplication Properties 1:44
• Multiplying by a Positive Number
• Example: Positive
• Multiplying by a Negative Number
• Example: Negative
• Division Properties 3:23
• Example: Positive
• Example: Negative
• Describing the Solution Set 6:00
• Set Builder Notation
• Graphing
• Lecture Example 1 8:04
• Lecture Example 2 9:09