Explanation Given: The inequality is 2 x x 2 − x − 6 ≥ 0 . Properties of Inequality: For all real numbers a , b , and c : 1. If a < b , then a + c < b + c . 2. If a < b and if c > 0 , then a c < b c . 3. If a < b and if c < 0 , then a c < b c . Express the given inequality as equation, 2 x x 2 − x − 6 = 0 . Rearrange the terms and simplify the terms as follows. ( x 2 − x − 6 ) ( 2 x x 2 − x − 6 ) = ( x 2 − x − 6 ) ( 0 ) 2 x = 0 x = 0 2 x = 0 Set the denominator equal to 0 and solve. x 2 − x − 6 = 0 x 2 + 2 x − 3 x − 6 = 0 x ( x + 2 ) − 3 ( x + 2 ) = 0 ( x + 2 ) ( x − 3 ) = 0 Therefore, by zero property, x = − 2 or x = 3 . Thus, the solutions determine two intervals on the number line: ( − ∞ , − 2 ) , ( − 2 , 0 ) , ( 0 , 3 ) and ( 3 , ∞ ) . Substitute a number from each interval into the original inequality. For the interval ( − ∞ , − 2 ) , choose −3 to test for the variable x . 2 x x 2 − x − 6 = 2 ( − 3 ) ( − 3 ) 2 − ( − 3 ) − 6 = − 6 9 + 3 − 6 = − 6 12 − 6 = − 1 Since −1 is not greater than or equal to 0, it is not considered as the solution

Finite Mathematics and Calculus with Applications

1st Edition

ISBN: 9781323188361

Author: Margaret Lial

Publisher: Pearson Education

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Chapter R.5, Problem 51E

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To solve: The inequality 2xx2−x−6≥0.

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Chapter R.5, Problem 50E

Chapter R.5, Problem 52E

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Finite Mathematics and Calculus with Applications

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The inequality 2 x x 2 − x − 6 ≥ 0 .

Solution Summary: The author explains how to solve the inequality, which is 2x2-x-6ge 0.

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