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: 31


$\{x\ |\ x\lt-7\}\cup\{x\ |\ x\gt21\}$

Work Step by Step

$2|x-7|\gt28\longrightarrow$ divide each side by 2 $2|x-7|\div2\gt28\div2\longrightarrow$ divide $|x-7|\gt14\longrightarrow$ write a compound inequality using the definition of absolute values $x-7\lt-14$ OR $x-7\gt14\longrightarrow$ solve each inequality $x-7\lt-14\longrightarrow$ add 7 to each side $x-7+7\lt-14+7\longrightarrow$ add $x\lt-7$ OR $x-7\gt14\longrightarrow$ add 7 to each side $x-7+7\gt14+7\longrightarrow$ add $x\gt21$ A compound inequality joined by OR is the union of the two solution sets.
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