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 R - Elementary Algebra Review - R.2 Equations, Inequalities, and Problem Solving - R.2 Exercise Set: 29

Answer

$a=-\dfrac{61}{115}$

Work Step by Step

Using the Distributive Property which is given by $a(b+c)=ab+ac,$ then \begin{array}{l}\require{cancel} 0.1(a-0.2)=1.2+2.4a \\\\ 0.1(a)+0.1(-0.2)=1.2+2.4a \\\\ 0.1a-0.02=1.2+2.4a .\end{array} Using the properties of equality, the equation above is equivalent to \begin{array}{l}\require{cancel} 0.1a-0.02=1.2+2.4a \\\\ 100(0.1a-0.02)=100(1.2+2.4a) \\\\ 10a-2=120+240a \\\\ 10a-240a=120+2 \\\\ -230a=122 \\\\ a=\dfrac{122}{-230} \\\\ a=\dfrac{\cancel2(61)}{\cancel2(-115)} \\\\ a=\dfrac{61}{-115} \\\\ a=-\dfrac{61}{115} .\end{array}
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