Answered: < 1 I> 3-x -1

Algebra: Structure And Method, Book 1

(REV)00th Edition

ISBN:9780395977224

Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Chapter2: Working With Real Numbers

Section2.4: Subtracting Real Numbers

Problem 12MRE

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The screenshot I attached solves for x in a geometric series. Could you please explain how you come up with the numbers -1<x<3. The question is #79 from chapter 9.2 in Universtiy Calculus Early Transcendentals fourth edition. Thank you so much

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$|\frac{6}{3 - x}| < 1 = > \frac{|6|}{|3 - x|} < 1 = > \frac{6}{|3 - x|} < 1 = > \frac{6}{|3 - x|} \times |3 - x| < 1 \times |3 - x| [∵ |3 - x| i s a l w a y s p o s i t i v e] = > 6 < |3 - x| = > |3 - x| > 6$

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