Intermediate Algebra (12th Edition)

Published by Pearson
ISBN 10: 0321969359
ISBN 13: 978-0-32196-935-4

Chapter 1 - Section 1.6 - Set Operations and Compound Inequalities - 1.6 Exercises - Page 109: 21

Answer

$(-\infty, 2]$ Refer to the graph below.

Work Step by Step

$x\le2$ includes the numbers that are less than or equal to $2$. $x\le5$ includes the numbers that are less than or equal to $5$. The conjunction "and" means intersection so find the numbers that are common to both inequalities. The intersection of the two given sets is the set of real numbers that are less than or equal to $2$. Hence, the solution set is $(-\infty, 2]$. Graph the solution set by plotting a solid dot at $2$ then shade the region to its left. (Refer to the graph above.)
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