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: 24

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 5 to both sides to have: $\\5(\frac{2}{5}x +1) \lt 5(\frac{1}{5}-2x) \\2x+5 \lt 1-10x$ Add $10x$ to both sides to have: $\\2x+5+10x \lt 1-10x+10x \\12x+5 \lt 1$ Subtract 5 to both sides to have: $\\12x+5-5 \lt 1 -5 \\12x \lt -4$ Divide 12 to both sides to have: $\\x \lt \frac{-4}{12} \\ x \lt -\frac{1}{3}$
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