Which of the following answers gives the best estimate for x given the following equation?

21x+1,998=2,243
21
𝑥
+
1
,
998
=
2
,
243

(1 point)
Responses

100
100

1,000
1,000

1
1

10..

1 answer

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.