What is the largest integer value of $x$ for which $5-4x>17$?
To solve this inequality, I want to isolate $x$ on one side of the inequality sign. I can start by subtracting $5$ from both sides, which gives me $-4x>12$. Then, I can divide both sides by $-4$, but I have to remember that dividing by a negative number reverses the inequality sign, so I get $x<-3$. This means that $x$ has to be less than $-3$, and the largest integer that satisfies this is $x=-4$. 