Explanation Procedure used: (1) . Find an equivalent inequality with 0 on one side. (2). Change the inequality symbol to an equals sign and solve the related equation. (3). Find values of the variables for which the related rational function is not defined. (4). The found in steps (2) and (3) are called the critical values. Use the critical values to divide the x axis into intervals. Then determine the function’s sign in each interval using an x value from the interval or using the graph of the equation. (5). Select the intervals for which the inequality is satisfied and write intervals notation or set builder notation for the solution set. If the inequality symbol ≤ or ≥ , then the solutions to step (2) should be include in the solution set. The x values found in step (3) are never include in the solution set. Calculation: The given rational inequality is 8 x x 2 − 4 ≥ 0 . By the procedure from 1 to 5, find the solution set of the inequality. Change the inequlity sign by equal sign to form related equation as 8 x x 2 − 4 = 0 . The rational equation is undefined at the points x = − 2 and x = 2 . From the graph, the x intercept of the related function occurs at x = 0

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Chapter 4.6, Problem 23E

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Chapter 4.6, Problem 22E

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The rational inequality 8 x x 2 − 4 ≥ 0 .

Solution Summary: The author explains how to solve the rational inequality 8x24ge 0 by changing the inequality symbol to an equals sign.

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