Introductory Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-805-X
ISBN 13: 978-0-13417-805-9

Chapter 5 - Cumulative Review Exercises - Page 417: 5


$$x = -\frac{5}{3}$$

Work Step by Step

First, multiply by the least common denominator to get rid of the fractions. The least common denominator, in this case, is $30$: $$30(\frac{x}{5} - \frac{1}{3}) = 30(\frac{x}{10} - \frac{1}{2})$$ Divide out common factors to get rid of the fractions: $$6x - 10 = 3x - 15$$ Subtract $3x$ from both sides to get the variable on one side of the equation: $$6x - 10 - 3x = -15$$ Combine variable terms: $$3x - 10 = -15$$ Add $10$ to both sides of the equation to get the constants on one side of the equation: $$3x = -5$$ Divide both sides by $3$ to solve for $x$: $$x = -\frac{5}{3}$$
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