Explanation Given Information: The inequality is 9 x 2 − 25 ≤ 0 . Formula used: According to the zero theorem, if a and b are real numbers, with a b = 0 , then, a = 0 or b = 0 To solve a quadratic inequality, perform the following steps: Step 1: The inequality is written as an equation. Step 2: Use the solution from Step 1 and determine the intervals, and graph them on a number line. Step 3: To determine the suitable intervals that satisfy the inequality substitute a test value from each interval into the original inequality. Step 4: Separately, consider the endpoints. If the end point is included then the inequality has the symbol ≤ or ≥ . Calculation: Consider the inequality, 9 x 2 − 25 ≤ 0 Factor the equation 9 x 2 − 25 = 0 , 9 x 2 − 25 = 0 ( 3 x ) 2 − 5 2 = 0 ( 3 x + 5 ) ( 3 x − 5 ) = 0 Recall that according to the zero theorem, if a and b are real numbers, with a b = 0 , then, a = 0 or b = 0 Apply it, Case I: When the term ( 3 x + 5 ) = 0 3 x + 5 = 0 x = − 5 3 Case II: When the term ( 3 x − 5 ) = 0 3 x − 5 = 0 x = 5 3 Thus, the numbers − 5 3 and 5 3 divide the number line into 3 intervals, Test the three intervals, by substituting a number from each interval in the inequality

Beginning and Intermediate Algebra (6th Edition)

6th Edition

ISBN: 9780321969163

Author: Margaret L. Lial, John Hornsby, Terry McGinnis

Publisher: PEARSON

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Chapter 11.8, Problem 16E

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To calculate: The solution set of the inequality 9x2−25≤0 and graph it.

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Chapter 11.8, Problem 15E

Chapter 11.8, Problem 17E

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Chapter 11 Solutions

Beginning and Intermediate Algebra (6th Edition)

Ch. 11.1 - Concept Check Answer each question. 1. Which of...Ch. 11.1 - Prob. 2E Ch. 11.1 - Prob. 3E Ch. 11.1 - Prob. 4E Ch. 11.1 - Solve each equation using the zero-factor...Ch. 11.1 - Prob. 6E Ch. 11.1 - Solve each equation using the zero-factor...Ch. 11.1 - Prob. 8E Ch. 11.1 - Solve each equation using the zero-factor...Ch. 11.1 - Prob. 10E

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The solution set of the inequality 9 x 2 − 25 ≤ 0 and graph it.

Solution Summary: The author calculates the solution set of the inequality 9x2-25le 0 and graphs it.

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Chapter 11 Solutions