Question

the sum of three consecutive even integers is 84. What is the smallest of these integers?

Answer 1

Let the three consecutive even integers be represented as \( x \), \( x + 2 \), and \( x + 4 \).

The sum of these integers can be set up as follows:

\[
x + (x + 2) + (x + 4) = 84
\]

Combining the terms gives:

\[
3x + 6 = 84
\]

Now, subtract 6 from both sides:

\[
3x = 78
\]

Next, divide both sides by 3:

\[
x = 26
\]

The three consecutive even integers are:

- \( x = 26 \)
- \( x + 2 = 28 \)
- \( x + 4 = 30 \)

Therefore, the smallest of these integers is:

\[
\boxed{26}
\]