College Algebra 7th Edition

Published by Brooks Cole

Chapter 1, Equations and Graphs - Chapter 1 Review - Exercises - Page 171: 107

Answer

$(-1.855, -0.597) \cup (0.452, 2)$ Refer to the image below for the graph.

Work Step by Step

To solve the given inequality graphically, perform the following steps: (1) Let each side of the equation represent a function then graph each function on the same coordinate plane. Graph $y=x^4-4x^2$ (the blue graph) and $y=\dfrac{1}{2}x-1$ (the red graph). (refer to the attached image in the answer part above for the graph) (2) Identify the region/s where the blue graph has a smaller value than the red graph. The interval/s that cover these regions make up the solution set of the given inequality. Note that the blue graph is lower than the red graph in the following intervals: $(-1.855, -0.597)$ and $(0.452, 2)$ This means that the value of $x^4-4x^2$ is less than the value of $\dfrac{1}{2}x-1$ in the intervals $(-1.855, -0.597)$ and $(0.452, 2)$ Since the inequality involves $\lt$, then the endpoints $-1.855, -0.597, 0.452,$ and $2$ are not part of the solution set. Therefore, the solution set is: $(-1.855, -0.597) \cup (0.452, 2)$

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