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: 25


$(-\infty, -18)$ Refer to the attached image for the graph.

Work Step by Step

For easier work, get rid of the fractions by multiplying the LCD of 6 to both sides to have: $\\6(\frac{1}{3}x +2) \lt 6(\frac{1}{6}x-1) \\2x+12 \lt x-6$ Subtract $x$ to both sides to have: $\\2x+12-x \lt x-6-x \\x+12 \lt -6$ Subtract $12$ to both sides to have: $\\x+12-12 \lt -6-12 \\x \lt -18$
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