1. Solving Absolute-Value, Compound, and Quadratic Inequalities

2. Reminder: Compound Inequalities The following are examples of how to algebraically write the following graphs: 0 4 0≤x<4 -1 2 x 2

3. REMINDER How to solve a one variable inequality.

4. Solving a 1 Variable Inequality 0 x x = 0 x = 3 7 < 12 13 < 12 TrueFalse Find the BoundaryTest Every Region Represent the solutions to the following inequality algebraically and on a number line. Change inequality to equality Solve Plot Boundary Point(s) Pick a point in each region Substitute into Original Shade True Region(s) Algebraic Solution Closed or Open Dot(s)? Graphical Solution

5. Apply this method to more complicated Ineqaulities

6. Solving an Absolute Value Inequality 0 x x = -2 x = 0 x = 6 4 > 3 2 > 34 > 3 True False True Find the BoundaryTest Every Region Represent the solutions to the following inequality algebraically and on a number line. Change inequality to equality Solve Plot Boundary Point(s) Pick a point in each region Substitute into Original Shade True Region(s) Algebraic Solution Closed or Open Dot(s)? Graphical Solution

7. Solving a Compound Inequality 0 x x = -3 x = 0 x = 4 -12<-14≤-2 -12<-8≤-2-12<0≤-2 False True False Find the BoundaryTest Every Region Represent the solutions to the following inequality algebraically and on a number line. Change inequality to two equalities Solve Both Plot Boundary Point(s) Pick a point in each region Substitute into Original Shade True Region(s) Algebraic Solution Closed or Open Dot(s)? Graphical Solution

8. Solving a Quadratic Inequality 0 x x = -4 x = 0 x = 2 9 < 4 1 < 49 ≤ 4 False True False Find the BoundaryTest Every Region Represent the solutions to the following inequality algebraically and on a number line. Change inequality to equality Solve Plot Boundary Point(s) Pick a point in each region Substitute into Original Shade True Region(s) Algebraic Solution Closed or Open Dot(s)? Graphical Solution