Intermediate Algebra: Connecting Concepts through Application

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

Chapter 7 - Rational Functions - 7.5 Solving Rational Equations - 7.5 Exercises: 4

Answer

$\color{blue}{-\dfrac{17}{15}}$

Work Step by Step

Multiply $3p+4$ to both sides of the equation to obtain: $10(3p+4) = \dfrac{6}{3p+4} \cdot (3p+4) \\10(3p)+10(4)=6 \\30p+40=6$ Subtract $40$ to both sides of the equation to obtain: $30p=6-40 \\30w=-34$ Divide $30$ to both sides to obtain: $p = -\frac{34}{30} \\p=-\frac{17}{15}$ Cheking: $10=\dfrac{6}{3p+4}? \\10 = \dfrac{6}{3\cdot(-\frac{17}{15})+4}? \\10=\dfrac{6}{-\frac{17}{5}+4}? \\10=\dfrac{6}{-\frac{17}{5} + \frac{20}{5}}? \\10=\dfrac{6}{\frac{3}{5}}? \\10=6 \cdot \frac{5}{3}? \\10=10$ Thus, the solution to the given equation is: $\color{blue}{-\dfrac{17}{15}}$.
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