Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 1 - Introduction to Algebraic Expressions - Study Summary - Practice Exercises - Page 75: 30



Work Step by Step

$\bf{\text{Solution Outline:}}$ Use the Distributive Property to simplify the given expression, $ 2m+n-3(5-m-2n) .$ Then combine like terms. $\bf{\text{Solution Details:}}$ Using the Distributive Property which is given by $a(b+c)=ab+ac,$ the expression above is equivalent to \begin{array}{l}\require{cancel} 2m+n-3(5-m-2n) \\\\= 2m+n-3(5)-3(-m)-3(-2n) \\\\= 2m+n-15+3m+6n .\end{array} By combining like terms, the expression above is equivalent to \begin{array}{l}\require{cancel} 2m+n-15+3m+6n \\\\= (2m+3m)+(n+6n)-15 \\\\= 5m+7n-15 .\end{array}
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