The largest integer value for a would be 2.
To do this problem, we need to input -1 for x and solve the equation for y.
2x + ax - 7 > -12
2(-1) + a(-1) - 7 > -12
-1a -9 > -12
-1a > -3
a < 3
The largest integer possible would be 2 because a must be less than 3.