Answer
$(-∞,-15)$
Work Step by Step
$\frac{-x+2}{2} - \frac{1-5x}{8} \lt -1$
Multiply both sides by LCD $8$
$8(\frac{-x+2}{2} - \frac{1-5x}{8} )\lt 8(-1)$
Using distributive property,
$8(\frac{-x+2}{2}) - 8(\frac{1-5x}{8} ) \lt -8$
$4(-x+2)-(1-5x) \lt -8$
$-4x+8-1+5x \lt -8$
$x+7 \lt -8$
Add $-7$ to both sides.
$x+7-7 \lt -8-7$
$x \lt -15$
Solution set in Interval Notation : $(-∞,-15)$