Advanced Algebra 2.3 | Mr. Bartos Website

Overview:

We turn our attention in this section to solving and graphing inequalities. An inequality tells us about the relative size of two values. Unlike the equations that we have previously observed, inequalities generally do not have a single solution; rather, the solution describes an entire range of values. Thus, it makes sense to find this region by graphing the inequalities. Graphing an inequality in 2-dimensional space (a graph with 2 variables) is similar to graphing an inequality on the number line. Both involve treating the inequality as an equation, solving the equation, and testing points. The solutions to an inequality can be found by observing how the function divides the xy-graph into two regions: one that satisfies the inequality, and one that does not. There are many applications for using inequalities. One application of inequalities involves the topic of linear programming. Linear programming is a process by which constraints are turned into inequalities and graphed, and a value is maximized or minimized. This is especially useful in economics, in which linear programming is used to maximize revenue, minimize cost, and maximize profit. Inequalities have other applications including being used to describe the relationship between any two quantities when one quantity "limits" the other. These relationships appear frequently in physics and chemistry, as well as in everyday life. Inequalities are also used to find viable values of variables against several constraints.

Day 40:

Pre-Req Review: Linear Inequalities Review

Day 41:

Notes: Solving Non-Linear Inequalities

Homework: Solving Non-Linear Inequalities

Homework Solutions: Solving Non-Linear Inequalities Key

Day 42:

Warm-Up: Solving and Graphing Linear Inequalities (Pre-Req)

Practice: More Solving Non-Linear Inequalities

Practice Solutions: More Solving Non-Linear Inequalities Key

Day 43:

Notes: Graphing Quadratic Inequalities