Final answer:
The inverse operation to adding 10 in the equation 3y + 10 + 1 is the subtraction of 10. It's the operation that reverses the addition and helps isolate the variable 'y'.
Step-by-step explanation:
The inverse operation to the disconnecting number (also known as the additive inverse) in the equation 3y + 10 + 1 is the operation that reverses the effect of adding 10 in the equation. Therefore, the inverse operation is subtraction of 10.
To isolate the variable 'y' in the equation, you would start by removing the additional numbers. First, you would subtract 10 from both sides of the equation to cancel out the +10. This leaves you with 3y + 1, getting you closer to isolating y. Thus, the correct answer is d) Subtraction of 10.