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 - Concept and Vocabulary Check - Page 137: 1


Fill the blanks with: 2, 5, 2, 5

Work Step by Step

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 $ is an annotation for "no border", so it is always accompanied by a parenthesis For example $[a,b) = \{x\ |\; a\leq x \lt b\ \ \}\\ (-6,\infty) = \{x\ |\; x \gt -6\ \ \}\\ (-\infty,3] = \{x\ |\; x \leq 3\ \ \}$ --- "[2..." means that the left border 2 is included, "... 5)" means that the right border 5 is excluded. The interval contains all real numbers between 2 and 5, $2\leq x \lt 5$
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