### Instruction: What is the greatest integer value of $x$ for which $5-4x>17$?### Response: To find the greatest integer value of $x$, I want to isolate $x$ on one side of the inequality and see what it is less than or greater than.
To do that, 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 direction of the inequality.
So I get $x<-3$.
The greatest integer value of $x$ that satisfies this inequality is $-4$, because if I use any larger integer, such as $-3$, then the inequality would not hold.