## College Algebra 7th Edition

Published by Brooks Cole

# Chapter 1, Equations and Graphs - Section 1.9 - Solving Equations and Inequalities Graphically - 1.9 Exercises - Page 159: 38

#### Answer

$(-\infty, -0.54) \cup (0.54, +\infty)$

#### Work Step by Step

Graph $y_1 =\sqrt{0.5x^2+1}$ (the orange graph) and $y_2=2|x|$ (the purple graph) on the same coordinate plane. (refer to the attached image below for the graph) The solution to the given inequality is the set of x-values for which $y_1 \le y_2$. Notice that $y_1$ (the orange graph) is less than or equal to $y_2$ in the following intervals: $(-\infty, -0.54)$ and $(0.54, +\infty)$ Thus, the solution to the given inequality is: $(-\infty, -0.54) \cup (0.54, +\infty)$

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