To solve the equation \( 3x + 7(x + 1) = 2(6x + 5) - 2x \), we will first simplify both sides.
Starting with the left side:
\[ 3x + 7(x + 1) = 3x + 7x + 7 = 10x + 7 \]
Now, simplifying the right side:
\[ 2(6x + 5) - 2x = 12x + 10 - 2x = 10x + 10 \]
Now we have:
\[ 10x + 7 = 10x + 10 \]
Next, we will subtract \( 10x \) from both sides:
\[ 7 = 10 \]
This is a contradiction, meaning that the left side will never equal the right side for any real value of \( x \).
Thus, the conclusion is that there is no solution for \( x \) in the equation \( 3x + 7(x + 1) = 2(6x + 5) - 2x \).