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: 19


$p\displaystyle \ \ \ >\ \ \ \frac{1}{5}$

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) ----------------------------- $3p-1<6p+2(p-1)\qquad \qquad $... parenheses $3p-1<6p+2p-2\qquad $... simplify RHS $3p-1<8p-2 \qquad \qquad $P1: ...$/-8p$ $-5p-1\ \ \ \frac{1}{5}$ In interval notation:$\qquad (\displaystyle \frac{1}{5}, \infty)$.
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