Introductory Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-805-X
ISBN 13: 978-0-13417-805-9

Chapter 1 - Section 1.4 - Basic Rules of Algebra - Exercise Set - Page 54: 65

Answer

$7+2(x+9)$ $=7+(2x+18)\quad $(distributive property) $=7+(18+2x)\quad $(addition: commutative property) $=(7+18)+2x\quad $(addition: associative property) $=25+2x\quad $(combining like terms, simplification of parentheses) $=2x+25\quad $(addition: commutative property)

Work Step by Step

Commutative properties: $a+b=b+a,\qquad ab=ba$ Associative properties:$ a+(b+c)=(a+b)+c,\qquad a(bc)=(ab)c$ Distributive property: $\quad A(x+y)=Ax+Ay$ Combine like terms by combining the coefficients of the terms and keeping the same variable factor. --- $7+2(x+9)$ $=7+(2x+18)\quad $(distributive property) $=7+(18+2x)\quad $(addition: commutative property) $=(7+18)+2x\quad $(addition: associative property) $=25+2x\quad $(combining like terms, simplification of parentheses) $=2x+25\quad $(addition: commutative property)
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