To determine the nature of the solution for the equation \( 3x + 7(x + 1) = 2(6x + 5) - 2x \), let's simplify both sides.
Start by expanding and simplifying:
Left Side:
\[ 3x + 7(x + 1) = 3x + 7x + 7 = 10x + 7 \]
Right Side:
\[ 2(6x + 5) - 2x = 12x + 10 - 2x = 10x + 10 \]
Now the equation looks like this:
\[ 10x + 7 = 10x + 10 \]
Next, we will isolate \( x \):
Subtract \( 10x \) from both sides:
\[ 7 = 10 \]
This statement is false, meaning that there are no values of \( x \) that satisfy the equation. Therefore, the answer is:
B. no solution.