Algebra 1

Published by Prentice Hall
ISBN 10: 0133500403
ISBN 13: 978-0-13350-040-0

Chapter 3 - Solving Inequalities - 3-8 Unions and Intersections of Sets - Practice and Problem-Solving Exercises - Page 219: 32


$\{t\ |\ t\geq-2.\overline3\}\cap\{t\ |\ t\leq3\}$

Work Step by Step

$|4.5t-1.5|\leq12\longrightarrow$ write and solve a compound inequality $-12\leq4.5t-1.5\leq12\longrightarrow$ add 1.5 to each part $-12+1.5\leq4.5t-1.5+1.5\leq12+1.5\longrightarrow$ add $-10.5\leq4.5t\leq13.5\longrightarrow$ divide each part by 4.5 $-10.5\div4.5\leq4.5t\div4.5\leq13.5\div4.5\longrightarrow$ divide $-2.\overline3\leq t\leq3$ This compound inequality can be rewritten as $t\geq-2.\overline3$ AND $t\leq3$ A compound inequality joined by AND can be written as the intersection of 2 sets.
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