Elementary Algebra

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

Chapter 4 - Proportions, Percents, and Solving Inequalities - 4.4 - Inequalities - Problem Set 4.4 - Page 169: 3

Answer

This inequality is false.

Work Step by Step

$\frac{2}{3}$ - $\frac{3}{4}$ + $\frac{1}{6}$ $\gt$ $\frac{1}{5}$ + $\frac{3}{4}$ - $\frac{7}{10}$ To check whether this inequality is true or false, we simplify it. We need to make the denominators the same in order to simplify this inequality. $\frac{2}{3}$ $\times$ $\frac{20}{20}$ - $\frac{3}{4}$ $\times$ $\frac{15}{15}$ + $\frac{1}{6}$ $\times$ $\frac{10}{10}$ $\gt$ $\frac{1}{5}$ $\times$ $\frac{12}{12}$ + $\frac{3}{4}$ $\times$ $\frac{15}{15}$- $\frac{7}{10}$ $\times$ $\frac{6}{6}$ $\frac{40}{60}$ - $\frac{45}{60}$ + $\frac{10}{60}$ $\gt$ $\frac{12}{60}$ + $\frac{45}{60}$ - $\frac{42}{60}$ $\frac{5}{60}$ $\gt$ $\frac{15}{60}$ Multiply both sides by 60 to obtain: 5 $\gt$ 15 Because 5 is not greater than 15, this inequality is false.
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