Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter P - Section P.9 - Linear Inequalities and Absolute Value Inequalities - Exercise Set - Page 137: 9


$\{x\ |\ \ x \geq -3 \ \}$

Work Step by Step

Recall the general rules for writing intervals: An interval may be annotated as $[a,b],\ (a,b],\ [a,b),\ (a,b),\ (-\infty,b],\ (-\infty,b),\ [a,\infty),\ (a,\infty).$ It contains numbers between the left and right borders. The inequality signs depend on whether a border is included in the set or not. The bracket "[", or "]" means "border included" and the sign is "$\leq $". The parenthesis "(" or ")" means "border excluded" and the sign is "$\lt $". $\pm\infty $ implies "no border", so it is always accompanied by a parenthesis. For example $[a,b)=\{x\ |\ a\leq x\lt b\ \}$ $(-6,\infty)=\{x\ |\ x\gt-6\ \}$ $(-\infty,3]=\{x\ |\ \ x\leq 3\ \}$ --- Here, the left border is included, and the right has no bounds. We write this as $-3 \leq x \lt \infty $ or, simply as: $\qquad x \geq -3.$ $[-3,\infty)$ = $\{x\ |\ \ x \geq -3 \ \}$
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