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: 18


$y\ \ \leq\ \ 1$

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) ----------------------------- $-2(3y-8)\geq 5(4y-2)$ ...expand parentheses $-6y+16\geq 20y-10\qquad \qquad $P1: ...$/-16$ $-6y\geq 20y-26\qquad \qquad $P1: ...$/-20y$ $-26y\geq-26 \qquad\qquad $P$3$: ...$/\div(-9)$... (negative) $y\ \ \leq\ \ 1$ In interval notation:$\qquad (-\infty, 1]$.
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