College Algebra (6th Edition)

Published by Pearson
ISBN 10: 0-32178-228-3
ISBN 13: 978-0-32178-228-1

Chapter 3 - Polynomial and Rational Functions - Concept and Vocabulary Check: 5

Answer

{x|$(-∞,-2)$U$[1,∞)$}

Work Step by Step

The first step to solving a radical inequality is to express it in a way so that one side is zero and the other side is a single quotient, which has already been done in this exercise: $$\frac{x-1}{x+2} \geq 0$$ We've also been given the values that define the intervals for the x-axis: $x = 1$ and $x = -2$. Since we're looking for values of $x$ that make the radical inequality $greater$ $than$ $or$ $equal$ $to$ $0$, we need to identify test values within each interval to determine if the result satisfies the conditions. Three adequate test values are $-3$, $0$ and $2$: $-3$ $$\frac{(-3)-1}{(-3)+2} = \frac{-4}{-1} = (+)$$ which means it satisfies the condition that the answer be greater than zero. $0$ $$\frac{(0) - 1}{(0) +2} = \frac{-1}{2} = (-)$$ which does not satisfy the condition that the answer be greater than zero. $2$ $$\frac{(2) - 1}{(2) + 2} = \frac{1}{4} = (+)$$ which satisfies the condition that the answer be greater than zero. Finally, taking into consideration that the inequality is undefined when $x = -2$, we can write the solution set of this inequality as $(-∞,-2)$U$[1,∞)$
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