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Solving Absolute-Value, Compound, and Quadratic Inequalities

Solving Absolute-Value, Compound, and Quadratic Inequalities. Reminder: Compound Inequalities. The following are examples of how to algebraically write the following graphs:. 0 ≤x<4. 0 4. x<-1 or x>2. -1 2. REMINDER. How to solve a one variable inequality.

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Solving Absolute-Value, Compound, and Quadratic Inequalities

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  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≤x<4 0 4 x<-1 or x>2 -1 2

  3. REMINDER How to solve a one variable inequality.

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

  5. Apply this method to more complicated Ineqaulities

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

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

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

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