Solving Absolute-Value, Compound, and Quadratic Inequalities

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

REMINDER How to solve a one variable inequality.

Solving a 1 Variable Inequality 0 x x = 0 x = 3 7 < < 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

Apply this method to more complicated Ineqaulities

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

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

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