## Intermediate Algebra (6th Edition)

Published by Pearson

# Chapter 2 - Section 2.4 - Linear Inequalities and Problem Solving - Exercise Set - Page 86: 67

#### Answer

$(-∞,5)$

#### Work Step by Step

$\frac{x+3}{12} + \frac{x-5}{15} \lt \frac{2}{3}$ LCD for $12, 15, 3$ is $60$ Multiply both sides by LCD, $60$ to eliminate fractions. $60(\frac{x+3}{12} + \frac{x-5}{15}) \lt \frac{2}{3} \times 60$ Applying distributive property, $60(\frac{x+3}{12}) + 60(\frac{x-5}{15}) \lt \frac{2}{3} \times 60$ $5(x+3)+4(x-5) \lt 40$ $5x+15+4x-20 \lt 40$ Combine like terms. $9x-5 \lt 40$ Add $5$ to both sides. $9x-5+5 \lt 40+5$ $9x \lt 45$ Divide by $9$ on both sides. $x \lt 5$ Solution set using interval notation :$(-∞,5)$

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