To solve the equation \( 2x + 5 = 2(x + 1) + 11 \), we'll first simplify the right side of the equation.
Start by expanding the right side:
\[ 2(x + 1) + 11 = 2x + 2 + 11 = 2x + 13 \]
Now, we can rewrite the equation:
\[ 2x + 5 = 2x + 13 \]
Next, we'll subtract \( 2x \) from both sides:
\[ 5 = 13 \]
This statement is false, which indicates that there are no values of \( x \) that can satisfy the original equation. Thus, the equation has no solution.