Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 6 - Test - Page 406: 25



Work Step by Step

By cross-multiplication, in terms of $x$, the given equation, $ \dfrac{x+b}{a}=\dfrac{4x-7a}{b} ,$ is equivalent to \begin{array}{l}\require{cancel} b(x+b)=a(4x-7a) \\\\ bx+b^2=4ax-7a^2 \\\\ bx-4ax=-7a^2-b^2 \\\\ x(b-4a)=-7a^2-b^2 \\\\ x=\dfrac{-7a^2-b^2}{b-4a} \\\\ x=\dfrac{-(7a^2+b^2)}{-(4a-b)} \\\\ x=\dfrac{7a^2+b^2}{4a-b} .\end{array}
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