SAT Question e723bd67: Linear Inequalities answer and explanation with Desmos solution

Choice D is correct. All the tables in the choices have the same three values of $x$, $440$, $441$, and $442$, so each of the three values of $x$ can be substituted in the given inequality to compare the corresponding values of $y$ in each of the tables. Substituting $440$ for $x$ in the given inequality yields $2\left(440\right)-y>883$, or $880-y>883$. Subtracting $880$ from both sides of this inequality yields $-y>3$. Dividing both sides of this inequality by $-1$ yields $y<-3$. Therefore, when $x=440$, the corresponding value of $y$ must be less than $-3$. Substituting $441$ for $x$ in the given inequality yields $2\left(441\right)-y>883$, or $882-y>883$. Subtracting $882$ from both sides of this inequality yields $-y>1$. Dividing both sides of this inequality by $-1$ yields $y<-1$. Therefore, when $x=441$, the corresponding value of $y$ must be less than $-1$. Substituting $442$ for $x$ in the given inequality yields $2\left(442\right)-y>883$, or $884-y>883$. Subtracting $884$ from both sides of this inequality yields $-y>-1$. Dividing both sides of this inequality by $-1$ yields $y<1$. Therefore, when $x=442$, the corresponding value of $y$ must be less than $1$. For the table in choice D, when $x=440$, the corresponding value of $y$ is $-4$, which is less than $-3$; when $x=441$, the corresponding value of $y$ is $-2$, which is less than $-1$; when $x=442$, the corresponding value of $y$ is $0$, which is less than $1$. Therefore, the table in choice D gives values of $x$ and their corresponding values of $y$ that are all solutions to the given inequality.