3.5 Polynomial and Rational Inequalities. Solving inequalities – true/false quiz True or False. 1.True or False. The solution set of is x > 4 2. True.

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Presentation transcript:

3.5 Polynomial and Rational Inequalities

Solving inequalities – true/false quiz True or False. 1.True or False. The solution set of is x > 4 2. True or False. The solution of is : x > -8 True or False. 1.True or False. The solution set of is x > 4 2. True or False. The solution of is : x > -8 BOTH are FALSE! You cannot multiply an inequality by an expression containing an unknown (x). BOTH are FALSE! You cannot multiply an inequality by an expression containing an unknown (x).

(-1.5,0) (2,0) 1. Solving Inequalities from the graph Solve the following using the graph.

1. Solving Inequalities from the graph Solve the following using the graph.

2. Solving Inequalities algebraically Step 1: Get all terms on one side. Rewrite as Step 2: Boundary points. if polynomial: x-intercepts if rational: x-intercepts and Vertical Asymptotes Step 2: Boundary points. if polynomial: x-intercepts if rational: x-intercepts and Vertical Asymptotes Step 3: Table of Intervals : Step 4: Test points in each interval Step 5: Choose intervals satisfying Step 1 Step 4: Test points in each interval Step 5: Choose intervals satisfying Step 1

Examples

Examples

Examples

3. Solving Rational Inequalities algebraically

3. Examples

Practice Problem