Intermediate Algebra: Connecting Concepts through Application

Published by Brooks Cole
ISBN 10: 0-53449-636-9
ISBN 13: 978-0-53449-636-4

Chapter 4 - Quadratic Functions - 4.5 Solving Equations by Factoring - 4.5 Exercises - Page 358: 9


$\color{blue}{\left\{-\frac{5}{7}, 0, \frac{8}{3}, 6\right\}}$.

Work Step by Step

RECALL: Zero-Factor Property: If $ab = 0$, then either $a=0$ or $b=0$ or both are $0$. Use the property above to obtain: \begin{array}{ccccc} &4.5w=0 &\text{or} &3w-8=0 &\text{or} &7w+5=0 &\text{or} &w-6=0 \end{array} Solve each equation to obtain: $4.5w=0 \\\frac{4.5w}{4.5}=\frac{0}{4.5} \\w=0$ or $3w-8=0 \\3w=8 \\\frac{3w}{3}=\frac{8}{3} \\w=\frac{8}{3}$ or $7w+5=0 \\7w=-5 \\\frac{7w}{7}=\frac{-5}{7} \\w=-\frac{5}{7}$ or $w-6=0 \\w=0+6 \\w=6$ Thus, the solution set is $\color{blue}{\left\{-\frac{5}{7}, 0, \frac{8}{3}, 6\right\}}$.
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