Explanation Given: The rational inequality is 3 2 − x > x 2 + x . Procedure used: Procedure to solve a rational inequality: 1. First rewrite the given inequality in such a way that 0 is on one side of the inequality and on the other side there must be single rational expression. 2. Determine the values of x which makes either the numerator or denominator equal to zero. These values of x form the interval on the number line. 3. Use a test value from each interval obtained in step 2 to check which interval is forming the solution set. Check the values at endpoints of the interval also. Calculations: Consider the given rational inequality 3 2 − x > x 2 + x . Step 1: The given rational inequality can be written as follows: 3 2 − x > x 2 + x 3 2 − x − x 2 + x > 0 3 ( 2 + x ) − x ( 2 − x ) ( 2 − x ) ( 2 + x ) > 0 x 2 + x + 6 ( 2 − x ) ( 2 + x ) > 0 Now the given rational inequality is x 2 + x + 6 ( 2 − x ) ( 2 + x ) > 0 . Step 2: The given rational expression is x 2 + x + 6 ( 2 − x ) ( 2 + x ) . Now the numerator of the above rational expression can never be zero since the roots of the quadratic equation are imaginary and the denominator is zero when ( 2 − x ) ( 2 + x ) = 0 . Thus, the denominator of the rational expression is zero when x = 2 and − 2

A Graphical Approach to College Algebra, Books a la Carte Edition (6th Edition)

6th Edition

ISBN: 9780321900715

Author: John Hornsby, Margaret L. Lial

Publisher: PEARSON

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Chapter 4.3, Problem 68E

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The solution set of the rational inequality 32−x>x2+x.

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Chapter 4.3, Problem 67E

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A Graphical Approach to College Algebra, Books a la Carte Edition (6th Edition)

Ch. 4.1 - Provide a short answer to each question. Do not...Ch. 4.1 - Prob. 2E Ch. 4.1 - Prob. 3E Ch. 4.1 - Prob. 4E Ch. 4.1 - Prob. 5E Ch. 4.1 - Provide a short answer to each question. Do not...Ch. 4.1 - Prob. 7E Ch. 4.1 - Prob. 8E Ch. 4.1 - Prob. 9E Ch. 4.1 - Prob. 10E

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The solution set of the rational inequality 3 2 − x &gt; x 2 + x .

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The solution set of the rational inequality 3 2 − x > x 2 + x .