What's under the square root radical cannot be negative,
so we have a critical number when x+7=0 or x=7.
First we solve the equation of the boundary
to find all other potential critical numbers besides -7.
Isolate the square root term on the left:
Square both sides:
From that we get critical values 2 and 9
We put all three critical values on a number line
-------o--------------------------o--------------------o------
-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11
So we test the original inequality in each of the intervals
Testing the inequality 
Choose test value -8 and substitute in the original inequality:
That's not a real number on the left, so we do not use that
interval.
Testing the inequality 
Choose test value 0 and substitute in the original inequality:
That's false, so we do not use that interval.
Testing the inequality 
Choose test value 3 and substitute in the original inequality:
That's false, so we do not use that interval.
Testing the inequality 
Choose test value 10 and substitute in the original inequality:
That's true, so we use that interval
Now we test the critical values themselves:
Testing critical value -7
That's false.
Testing critical value 2
That's false.
Testing critical value 9
That's false. So the interval is open at 9
Answer:
Edwin
