To isolate the variable \( x \) and get rid of the \( x \) on the right side of the equation, you can subtract \( x \) from each side. This will keep the equation balanced.
So the correct move is:
A. Subtract \( x \) from each side.
This simplifies the equation as follows:
\[ x - x = x + 1 - x \]
Which results in:
\[ 0 = 1 \]
This indicates that the original equation \( x = x + 1 \) has no solutions.