Discrete Mathematics with Applications 4th Edition

Published by Cengage Learning
ISBN 10: 0-49539-132-8
ISBN 13: 978-0-49539-132-6

Chapter 4 - Elementary Number Theory and Methods of Proof - Exercise Set 4.2 - Page 169: 28


Yes, x is rational. $x = \frac{d-b}{a-c}$

Work Step by Step

Expanding, we get $ax+b = cx+d, ax-cx = d-b, (a-c)x = d-b, x = \frac{d-b}{a-c}$. Since $a,b,c,d$ are all integers, $x$ is the ratio of an integer to another integer, so it must be rational, so the statement is proven.
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