To solve the equation \( 21x + 1,998 = 2,243 \), we first subtract 1,998 from both sides:
\[ 21x = 2,243 - 1,998 \]
Calculating the right side:
\[ 2,243 - 1,998 = 245 \]
Now the equation simplifies to:
\[ 21x = 245 \]
Next, we divide both sides by 21 to solve for \( x \):
\[ x = \frac{245}{21} \]
Calculating the division:
\[ x = \frac{245 \div 7}{21 \div 7} = \frac{35}{3} \approx 11.67 \]
Given the choices presented, the closest estimate for \( x \) is 10.