Simple question

First consider
x < ( x + 10 ) / 2
2x < x + 10
x < 10
Next consider 122 > x2 > 63.
For x is an integer, the smallest value of x which can satisfy the condition is 8 since 82 = 64.
The greatest value of x which can satisfy the condition is 11 since 112 = 121.
From that, 7 < x < 12.
Lastly, by combination, 7 < x < 10.