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