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Solving Nonlinear Inequalities Steps (Multiple Examples) End ShowEnd Show Slide #1 NextNext The following steps can be applied to the following types of.

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Presentation on theme: "Solving Nonlinear Inequalities Steps (Multiple Examples) End ShowEnd Show Slide #1 NextNext The following steps can be applied to the following types of."— Presentation transcript:

1 Solving Nonlinear Inequalities Steps (Multiple Examples) End ShowEnd Show Slide #1 NextNext The following steps can be applied to the following types of nonlinear inequalities as well as others. Polynomial Rational Exponential Logarithmic Radical (Root) Trigonometric Unfortunately with showing 6 examples, there isn't enough room on each slide to show the work from previous slides. So you may want to note results from previous slides for the example you're following.

2 Solving Nonlinear Inequalities Steps (Multiple Examples) PreviousPrevious Slide #2 NextNext Step #1:Related Equation Solve the related equation to find when both side are equal. Examples PolynomialRationalExponentialRadicalLogarithmicTrigonometric

3 Solving Nonlinear Inequalities Steps (Multiple Examples) PreviousPrevious Slide #3 NextNext Step #2:Domain Find domain restrictions to find out where the inequality is undefined. Examples PolynomialRationalExponentialRadicalLogarithmicTrigonometric

4 Solving Nonlinear Inequalities Steps (Multiple Examples) PreviousPrevious Slide #4 NextNext Step #3:Real Line Set up the intervals on a real line using endpoints from both the solutions to the related equation and the domain. Examples PolynomialRationalExponentialRadicalLogarithmicTrigonometric

5 Solving Nonlinear Inequalities Steps (Multiple Examples) PreviousPrevious Slide #5 NextNext Step #4:Intervals Decide which intervals should be included based on either a sign graph, test points, or a calculator's graph. I'll use the calculator's graph for the examples. Examples PolynomialRationalExponentialRadicalLogarithmicTrigonometric

6 Solving Nonlinear Inequalities Steps (Multiple Examples) PreviousPrevious Slide #6 NextNext Step #5:Endpoints For each endpoint, determine whether it is included or not based on the domain restrictions, and whether it is a strict inequality or not. Examples PolynomialRationalExponentialRadicalLogarithmicTrigonometric

7 Solving Nonlinear Inequalities Steps (Multiple Examples) PreviousPrevious Slide #7 Restart End ShowRestart End Show Step #6:Solution Set Finally, give the solution set. Examples PolynomialRationalExponentialRadicalLogarithmicTrigonometric

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