Elementary Algebra

Published by Cengage Learning
ISBN 10: 1285194055
ISBN 13: 978-1-28519-405-9

Chapter 7 - Algebraic Fractions - 7.5 - Fractional Equations and Problem Solving - Problem Set 7.5: 6

Answer

{$3$}

Work Step by Step

First, we add the two fractions on the left hand side of the equation by finding the LCM of the denominators of the two fractions. Upon observation, we find that the LCM of the two denominators is 21. Then, we cross multiply the resultant fractional equation and solve the resultant expression. Step 1: $\frac{n+2}{7}+\frac{n}{3}=\frac{12}{7}$ Step 2: $\frac{3(n+2)+7(n)}{21}=\frac{12}{7}$ Step 3: $\frac{3n+6+7n}{21}=\frac{12}{7}$ Step 4: $\frac{10n+6}{21}=\frac{12}{7}$ Step 5: $7(10n+6)=12(21)$ Step 6: $10n+6=12(3)$ Step 7: $10n=36-6$ Step 8: $10n=30$ Step 9: $n=3$ Therefore, the solution set is {$3$}.
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