Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 6 - Algebra: Equations and Inequalities - 6.2 Linear Equations in One Variable and Proportions - Exercise Set 6.2 - Page 362: 86


The solution set is \[\varnothing \](the empty set).

Work Step by Step

The equation is\[\frac{x}{4}+3=\frac{x}{4}\]. Subtract \[\frac{x}{4}\] from both sides of the equal sign. \[\begin{align} & \frac{x}{4}+3-\frac{x}{4}=\frac{x}{4}-\frac{x}{4} \\ & 3=0 \end{align}\] Therefore, the equation \[\frac{x}{4}+3=\frac{x}{4}\] is equivalent to the statement \[3=0\]. Which is false for every value of \[x\]. Thus, the equation has no solution. The solution set is \[\varnothing \](the empty set).
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