Choice Dhoice C is the correct answer.

1. Start with the equation: $10x + 10 = 110$
2. Subtract 10 from both sides: $10x = 110 - 10$
3. Simplify: $10x = 100$
4. Divide both sides by 10: $x = \frac{100}{10}$
5. Simplify: $x = 10$
6. Verify: $10(10) + 10 = 100 + 10 = 110$ ✓

Choice Dhoice D is incorrect because this results from adding 10 to 110: $120$, then $120/10 = 12$. Wrong inverse operation.

Choice Dhoice A is incorrect because this is the value of $10x$. You need to divide by 10.

Choice Dhoice C is incorrect because this results from multiplying 100 by 10: $1000$.