College Algebra 7th Edition

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

Chapter 1, Equations and Graphs - Chapter 1 Review - Exercises: 106

Answer

$(5.065, +\infty)$ Refer to the image below for the graph.
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Work Step by Step

To solve the given inequality graphically, perform the following steps: (1) Subtract $2$ on both sides of the inequality to obtain: $x^3-4x^2-5x-2\gt 0$ Graph this inequality using a graphing utility. (refer to the attached image in the answer part above for the graph) (2) Identify the region/s where the graph is above the x-axis. These are the regions where the value of $x^3-4x^2-5x-2$ is greater than $0$. Note that the graph is above the x-axis in the interval $(5.065, +\infty)$. Since the inequality involves $\gt$, then the endpoint $5.065$ is not part of the solution set. Therefore, the solution set is: $\color{blue}{(5.065, +\infty)}$
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