Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

APPENDIX A - Numbers, Inequalities, and Absolute Values - A Exercises - Page A10: 62


If $~~\vert x+3 \vert \lt \frac{1}{2}~~$ then $~~\vert 4x+13 \vert \lt 3$

Work Step by Step

Suppose that $\vert x+3 \vert \lt \frac{1}{2}$ Then: $\vert x+3 \vert \lt \frac{1}{2}$ $-\frac{1}{2} \lt x+3 \lt \frac{1}{2}$ $-2 \lt 4x+12 \lt 2$ $-1 \lt 4x+13 \lt 3$ $-3 \lt -1 \lt 4x+13 \lt 3$ $\vert 4x+13 \vert \lt 3$
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