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: 105

Answer

$\color{blue}{[1, 3]}$ 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) Let each side of the equation represent a function then graph each function on the same coordinate plane. Graph $y=4x-3$ (the blue graph) and $y=x^2$ (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 greater 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 higher than the red graph from $x=1$ to $x=3$. This means that the value of $4x-3$ is greater than or equal to the value of $x^2$ in the interval $(1. 3)$. Since the inequality involves $\ge$, then the endpoints $1$ and $3$ are part of the solution set. Therefore, the solution set is: $\color{blue}{[1, 3]}$
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