Let's solve the equation given:
\[ 2x + 7 = 2x + 8 \]
To find how many solutions this equation has, we can start by simplifying it. Subtract \( 2x \) from both sides:
\[ 7 = 8 \]
This statement is clearly false, which indicates that there are no values for \( x \) that can satisfy the equation.
Thus, the answer is:
No Solution.