Calculus with Applications (10th Edition)

Published by Pearson
ISBN 10: 0321749006
ISBN 13: 978-0-32174-900-0

Chapter R - Algebra Reference - R.5 Inequalities - R.5 Exercises - Page R-21: 17



Work Step by Step

Applying the properties of inequality, we can P1. add any number to both sides, P2. multiply (or divide) both sides with a positive $\quad $ number to arrive at a valid inequality. $\quad $ If we P3. multiply multiply (or divide) both sides with a negative number, we must change the direction of the inequality sign, to arrive at a valid inequality.. Our goal is to, step by step, isolate the unknown on one side and interpret the result (which, if any, will be an interval) ----------------------------- $m-(3m-2)+6<7m-19\qquad $ ...expand parentheses $m-3m+2+6<7m-19\qquad $... simplify the LHS $-2m+8<7m-19 \qquad $P1: ...$/-7m$ $-9m+8\ \ \frac{-27}{-9}$ $m>3$ In interval notation:$\qquad ($3, $\infty)$.
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