Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 1 - Section 1.8 - Inequalities - 1.8 Exercises - Page 89: 26

Answer

$(-\infty, \frac{1}{3}]$ Refer to the attached image below for the graph.
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Work Step by Step

For easier work, get rid of the fractions by multiplying the LCD of 6 to both sides to have: $\\6(\frac{2}{3}-\frac{1}{2}x) \ge 6(\frac{1}{6}+x) \\4-3x \ge 1+6x$ Add $3x$ to both sides to have: $\\4-3x+3x \ge 1+6x+3x \\4 \ge 1+9x$ Subtract 1 to both sides to have: $\\4-1 \ge 1+9x-1 \\3 \ge 9x$ Divide 9 to both sides to have: $\frac{3}{9} \ge x \\\frac{1}{3} \ge x \\x \le \frac{1}{3}$
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