Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 1 - Equations and Inequalities - 1.8 Absolute Value Equations and Inequalities - 1.8 Exercises: 15

Answer

The solutions are $x=\dfrac{7}{2}$ and $x=\dfrac{5}{2}$

Work Step by Step

$\Big|\dfrac{5}{x-3}\Big|=10$ Solving this absolute value equation is equivalent to solving two separate equations, which are: $\dfrac{5}{x-3}=10$ and $\dfrac{5}{x-3}=-10$ Solve the first equation: $\dfrac{5}{x-3}=10$ Take $x-3$ to multiply the right side: $5=10(x-3)$ $5=10x-30$ Solve for $x$: $-10x=-5-30$ $-10x=-35$ $x=\dfrac{-35}{-10}$ $x=\dfrac{7}{2}$ Solve the second equation: $\dfrac{5}{x-3}=-10$ Take $x-3$ to multiply the right side: $5=-10(x-3)$ $5=-10x+30$ Solve for $x$: $10x=30-5$ $10x=25$ $x=\dfrac{25}{10}$ $x=\dfrac{5}{2}$ The solutions are $x=\dfrac{7}{2}$ and $x=\dfrac{5}{2}$
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