Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Appendices - Section A.1 - Real Numbers and the Real Line - Exercises A.1 - Page AP-6: 16

Answer

$x\in(-\infty,-0)\cup(2,\infty)$
1583189808

Work Step by Step

Use properties from the table 'Absolute Values and Intervals". Applying Property 7: $|x|\gt a\quad\Leftrightarrow\quad x\gt a\ \ $or$\ \ x\lt-a, \quad $ for a = positive number We have $\begin{array}{ll} 1-x\gt 1 & /-1\\ -x\gt0 & /\times(-1)\\ x\lt 0 & \end{array}$ $\ \ $ or $\ \ $ $\begin{array}{ll} 1-x\lt -1 & /-1\\ -x\lt -2 & /\times(-1)\\ x\gt2 & \\ & \end{array}$ In interval form, we can write this result as $x\in(-\infty,-0)\cup(2,\infty)$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.