Answer:
[tex]-15y+9<-36\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:y>3\:\\ \:\mathrm{Interval\:Notation:}&\:\left(3,\:\infty \:\right)\end{bmatrix}[/tex]
Therefore, the first choice is correct.
The graph of the inequality is also attached below.
Step-by-step explanation:
Considering the inequality
[tex]-15y+9<-36[/tex]
solving
[tex]-15y+9<-36[/tex]
[tex]\mathrm{Subtract\:}9\mathrm{\:from\:both\:sides}[/tex]
[tex]-15y+9-9<-36-9[/tex]
[tex]-15y<-45[/tex]
[tex]\mathrm{Multiply\:both\:sides\:by\:-1\:\left(reverse\:the\:inequality\right)}[/tex]
[tex]\left(-15y\right)\left(-1\right)>\left(-45\right)\left(-1\right)[/tex]
[tex]15y>45[/tex]
[tex]\mathrm{Divide\:both\:sides\:by\:}15[/tex]
[tex]\frac{15y}{15}>\frac{45}{15}[/tex]
[tex]y>3[/tex]
In other words,
[tex]-15y+9<-36\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:y>3\:\\ \:\mathrm{Interval\:Notation:}&\:\left(3,\:\infty \:\right)\end{bmatrix}[/tex]
Therefore, the first choice is correct.
The graph of the inequality is also attached below.
