1. **State the problem:** We need to find three consecutive even integers whose sum is 24.
2. **Define variables:** Let the first even integer be $x$. Then the next two consecutive even integers are $x+2$ and $x+4$.
3. **Set up the equation:** The sum of these integers is given as:
$$x + (x+2) + (x+4) = 24$$
4. **Simplify the equation:**
$$3x + 6 = 24$$
5. **Solve for $x$:**
$$3x = 24 - 6$$
$$3x = 18$$
$$x = \frac{18}{3} = 6$$
6. **Find the integers:**
The integers are $6$, $8$, and $10$.
7. **Check the sum:**
$$6 + 8 + 10 = 24$$ which matches the problem statement.
**Final answer:** The three consecutive even integers are $6$, $8$, and $10$.
Consecutive Even Integers
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