College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 1, Equations and Graphs - Section 1.7 - Solving Inequalities - 1.7 Exercises: 10

Answer

$-1, 0, \frac{2}{3}, \frac{5}{6}, 1$

Work Step by Step

Subtract 2 to both sides of the inequality to obtain: $x^2+2-2\lt 4-2 \\x^2 \lt 2$ Thus, the numbers that will satisfy the given inequality are the ones whose squares are less than $2$. Note that among the elements of $S$, the following have squares that are less than 2: $(-1)^2=1 \\0^2=0 \\(\frac{2}{3})^2=\frac{4}{9} \\(\frac{5}{6})^2=\frac{25}{36} \\1^2=1$ Therefore, the elements of $S$ that satisfy the given inequality are: $-1, 0, \frac{2}{3}, \frac{5}{6}, 1$
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