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 polynomial inequality is ( x − 2 ) − 3 < 0 . Rewrite the rational equation as 1 ( x − 2 ) 3 < 0 . Let the rational function denoted by f ( x ) = 1 ( x − 2 ) 3 . Since the expression ( x − 2 ) 3 ≤ 0 for all values of x , then 1 ( x − 2 ) 3 < 0 is true for all values of x except the point x = 2 . Thus, the critical values of the rational equation is 2 . The critical values divide the x axis into the intervals as ( − ∞ , 2 ) and ( 2 , ∞ ) . Find the sign of the rational function on each interval by selecting test value as follows. Let the polynomial function is denoted by g ( x ) = 1 ( x − 2 ) 3

6th Edition

ISBN: 9780135962312

Author: BITTINGER

Publisher: PEARSON

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Chapter 4, Problem 89RE

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To solve: The rational inequality (x−2)−3<0.

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Chapter 4, Problem 88RE

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