In the Solving Inequalities lesson, Dr. Eaton covers first the properties of inequalities such as the addition property and subtraction property. After several examples of each, you will then learn about the multiplication and division properties and how positive and negative numbers influence how you solve the problem. Finally, you will describe the solution set with either set builder notation or graphing. Four extra examples round out this lecture.
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.
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.