1122. - > 1. (Hint: Use a guess-and-checkapproach.)

Name: 1122. - > 1. (Hint: Use a guess-and-checkapproach.)
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Description: 1122. - > 1. (Hint: Use a guess-and-checkapproach.)

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Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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122. - > 1. (Hint: Use a guess-and-check
approach.)

Expert Solution

Given,

$\frac{1}{x} > 1$

For all negative values of x, the left hand side of the inequality will be negative.

Therefore the values of x must be positive.

The left hand side is undefined when x = 0. Therefore the values of x must be greater than 0.

Now let x = 0.5, then

$\begin{array}{rcl} \frac{1}{x} & = & \frac{1}{0.5} \\ = & 2 > 1 \end{array}$

Let x = 1, then

$\begin{array}{rcl} \frac{1}{x} & = & \frac{1}{1} \\ = & 1 ≯ 1 \end{array}$

Hence the given inequality is true for all the values of x lying between 0 & 1.

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