Introductory Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-805-X
ISBN 13: 978-0-13417-805-9

Chapter 2 - Section 2.7 - Solving Linear Inequalities - Exercise Set - Page 195: 18

Answer

Interval Notation: $(-\infty, 1]$ Refer to the image below for the graph.
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Work Step by Step

The solution set of the given inequality includes all the numbers that are less than or equal to $1$. The set includes all the numbers to the left of $1$ so $-\infty$ will be used on the left side of the interval notation. The highest number in the set is $1$ so a bracket will be used on the right side of the interval. Thus, the interval notation equivalent of the given inequality is: $(-\infty, 1]$. To graph the solution set on a number line, plot a solid dot at $x=1$ then shade the region to its left. (refer to the attached image in the answer part above)
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