## Elementary Algebra

Published by Cengage Learning

# Chapter 4 - Proportions, Percents, and Solving Inequalities - Chapters 1-4 Cumulative Review Problem Set - Page 186: 42

#### Answer

The solution set is {x|x $\geq$ 21} , or [21,$\infty$) in interval notation.

#### Work Step by Step

Use the properties of inequalities to solve this inequality. $\frac{2}{7}$x - $\frac{1}{4}$ $\geq$ $\frac{1}{4}$x + $\frac{1}{2}$ $\frac{2x}{7}$ - $\frac{1}{4}$ $\geq$ $\frac{x}{4}$ + $\frac{1}{2}$ Add $\frac{1}{4}$ to both sides. $\frac{2x}{7}$ $\geq$ $\frac{x}{4}$ + $\frac{1}{2}$ + $\frac{1}{4}$ $\frac{2x}{7}$ $\geq$ $\frac{x+1}{4}$ + $\frac{1}{2}$ The least common multiple, or LCM, of 7, 4, and 2 is 28. Multiply both sides by the LCM. $\frac{2x}{7}$ $\times$ 28 $\geq$ $\frac{x+1}{4}$ $\times$ 28 + $\frac{1}{2}$ $\times$ 28 2x $\times$ 4 $\geq$ (x + 1) $\times$ 7 + 1 $\times$ 14 Use the distributive property. 8x $\geq$ 7x + 7 + 14 Subtract 7x from both sides. x $\geq$ 21 The solution set is {x|x $\geq$ 21} , or [21,$\infty$) in interval notation.

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