1. 3.5 Polynomial and Rational Inequalities

2. 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).

3. (-1.5,0) (2,0) 1. Solving Inequalities from the graph Solve the following using the graph.

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

5. 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

6. Examples

7. Examples

8. Examples

9. 3. Solving Rational Inequalities algebraically

10. 3. Examples

12. Practice Problem