Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 2 - Section 2.4 - Linear Inequalities and Problem Solving - Exercise Set - Page 85: 32



Work Step by Step

$\frac{1-2x}{3} + \frac{3x+7}{7} \gt 1$ Multiply both sides by the LCD, $21$ to clear fractions. $21(\frac{1-2x}{3} + \frac{3x+7}{7} ) \gt 21 (1)$ Applying distributive property, $21(\frac{1-2x}{3}) +21( \frac{3x+7}{7} ) \gt 21$ $7(1-2x) +3(3x+7) \gt 21$ Applying distributive property again, $7-14x+9x+21 \gt 21$ $-5x+28 \gt 21$ Add $-28$ on both sides. $-5x+28-28 \gt 21-28$ $-5x \gt -7$ Divide both sides by $-5$ and reverse the inequility symbol. $\frac{-5x}{-5} \lt \frac{-7}{-5}$ $x \lt \frac{7}{5}$ In interval notation $(-∞,\frac{7}{5})$
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