Answer
The solution is $[-8,5)$
Work Step by Step
$\frac{2y+3}{y-5} \leq 1$
First solve the corresponding equation
$\frac{2y+3}{y-5}=1$
$2y+3=y-5$
$y=-8$
For $(-\infty,-8)$, choose $-10$: $\frac{2(-10)+3}{(-10)-5}=\frac{17}{15} \gt 1$
For $(-8,5)$, choose $0$: $\frac{2(0)+3}{0-5}=\frac{-3}{5} \lt 1$
For $(5,\infty)$, choose $6:$, $\frac{2(6)+3}{6-5}=15\gt1$
The solution is $[-8,5)$
