The sum of three consecutive integers is -96. what is the largest integer?

You make the smallest integer, because you don't know what it is. Then to find the sum of the consecutive integers, you set up the equation, x+(x+1)+(x+2)=-96. Then you solve for x.
3x+3=96
3x=93
x=31
But x is the smallest number so you need to add 2 to x to get the largest integer. 
So the largest integer is 33.
Hope this helps.