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

21x + 1,998 = 2,243

1,000

100

10

1

1 answer

To solve the equation \( 21x + 1,998 = 2,243 \), we'll first isolate \( x \).

  1. Subtract \( 1,998 \) from both sides:

\[ 21x = 2,243 - 1,998 \]

  1. Calculate the right side:

\[ 2,243 - 1,998 = 245 \]

So now we have:

\[ 21x = 245 \]

  1. Divide both sides by \( 21 \):

\[ x = \frac{245}{21} \]

  1. Perform the division:

\[ x \approx 11.67 \]

Now, given the choices (1, 10, 100, 1,000), the best estimate for \( x \) is \( 10 \), as it is the closest to \( 11.67 \).

Thus, the best estimate for \( x \) is:

10