Intermediate Algebra (12th Edition)

Published by Pearson
ISBN 10: 0321969359
ISBN 13: 978-0-32196-935-4

Chapter 5 - Section 5.5 - Solving Equations by the Zero-Factor Property - 5.5 Exercises - Page 355: 5


$k=\left\{ -\dfrac{8}{3},\dfrac{5}{2} \right\}$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To solve the given equation, $ (2k-5)(3k+8)=0 ,$ use the Zero-Factor Property by equating each factor to zero. Then solve each equation. $\bf{\text{Solution Details:}}$ Equating each factor of the equation above to zero (Zero-Factor Property), then \begin{array}{l}\require{cancel} 2k-5=0 \text{ OR } 3k+8=0 .\end{array} Using the properties of equality to solve each of the equation above results to \begin{array}{l}\require{cancel} 2k-5=0 \\\\ 2k=5 \\\\ k=\dfrac{5}{2} \\\\\text{ OR }\\\\ 3k+8=0 \\\\ 3k=-8 \\\\ k=-\dfrac{8}{3} .\end{array} Hence, the solutions are $ k=\left\{ -\dfrac{8}{3},\dfrac{5}{2} \right\} .$
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