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: 27

Answer

$\{x\ |\ -3\lt x\}\cap\{x\ |\ x\lt6\frac{1}{3}\}$

Work Step by Step

$|3x-5|\lt14\longrightarrow$ write and solve a compound inequality $-14\lt3x-5$ AND $3x-5\lt14$ $-14\lt3x-5\longrightarrow$ add 5 to each side $-14+5\lt3x-5+5\longrightarrow$ add $-9\lt3x\longrightarrow$ divide each side by 3 $-9\div3\lt3x\longrightarrow$ divide $-3\lt x$ AND $3x-5\lt14\longrightarrow$ add 5 to each side $3x-5+5\lt14+5\longrightarrow$ add $3x\lt19\longrightarrow$ divide each side by 3 $3x\div3\lt19\div3\longrightarrow$ divide $x\lt6\frac{1}{3}$ The solution of a compound inequality joined by AND is the intersection of the inequalities.
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