The square root of 2x is greater than 3 and less than 4. How many integer values of x satisfy this condition?

$3\lt\sqrt{2x}\lt4\\~\\ 3^2\lt(\sqrt{2x}\ )^2\lt4^2\\~\\ 9\lt2x\lt16\\~\\ \frac92\lt\frac{2x}{2}\lt\frac{16}{2}\\~\\ 4.5 \lt x \lt 8$

The integers between 4.5 and 8 exclusively are:

5, 6, 7

So there are 3 different integer values of  x  that satisfy the condition.

Check: https://www.wolframalpha.com/input/?i=3%3Csqrt%282x%29%3C4