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 :$(-∞,5)$