Answer
$(\frac{-4}{3},\frac{7}{3})$
Work Step by Step
$\frac{1}{15} \lt \frac{8-3x}{15} \lt \frac{4}{5}$
Using the properties of inequalities,
Multiply all parts by the LCD 15.
$15(\frac{1}{15}) \lt 15(\frac{8-3x}{15}) \lt 15(\frac{4}{5})$
$1 \lt 8-3x \lt 12$
Add $-8$ to all parts.
$1-8 \lt 8-3x-8 \lt 12-8$
$-7 \lt -3x \lt4$
Divide by $-3$ and reverse the inequality symbol
$\frac{-7}{-3} \gt \frac{-3x}{-3} \gt \frac{4}{-3}$
$\frac{7}{3} \gt x \gt \frac{-4}{3}$
This is equal to
$\frac{-4}{3} \lt x \lt \frac{7}{3}$
Interval Notation: $(\frac{-4}{3},\frac{7}{3})$
