To determine how many solutions exist for the equation 3x + 13 = 3x + 6 + 1, we first simplify the equation.
Starting with the right side:
3x + 6 + 1 = 3x + 7
This turns our equation into:
3x + 13 = 3x + 7
Next, we can subtract 3x from both sides:
13 = 7
This statement is not true, as 13 is not equal to 7. This means the equation has no solutions.
Therefore, the answer is that there are zero solutions for this equation.