Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 10 - Section 10.4 - Nonlinear Inequalities and Systems of Inequalities - Exercise Set - Page 629: 46

Answer

Answers vary. Nonlinear inequalities can cover a finite range, while linear inequalities of only one function typically cover an infinite area.

Work Step by Step

Consider the example provided. For the linear function, the area that satisfies the inequality is infinite as it is the entire area on one side of the line. However, with the nonlinear inequality, the only area which satisfies the inequality is the area inside of the circle of radius 3. Thus, we see that linear inequalities almost always cover an infinite range while nonlinear inequalities can cover finite ranges.
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