x < -7 means
x is less than -7, not -7, but less.
Let's look at a number line:
This shows the solution set of the equation.
The open circle at -7 tells us that -7 IS NOT INCLUDED, but everything less than that is included.
We want the largest integer out of the solution.
THe integers are:
-8, -9, -10 ... and so on ...
The largest of them is
-8
