Nonlinear Inequalities

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Define nonlinear inequality.

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What is interval notation?

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How do you solve a nonlinear inequality?

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To solve a nonlinear inequality, follow these steps: 1. Rearrange the inequality to one side, setting it to zero. 2. Identify critical points by solving the corresponding equation. 3. Test intervals between critical points to determine where the inequality holds true. 4. Express the solution in interval notation.

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What is the significance of critical points in solving inequalities?

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Critical points are values where the expression equals zero or is undefined. They are significant because they divide the number line into intervals, allowing us to test each interval to determine where the inequality holds true.

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Explain the concept of testing intervals in inequalities.

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Testing intervals involves selecting test points from each interval created by critical points to determine if the inequality is satisfied in that interval. If the test point satisfies the inequality, then all values in that interval are part of the solution.

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Define a rational inequality.

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