To solve for three consecutive even integers whose sum is $18$, follow these steps:

Step 1: Represent the integers

Let the three consecutive even integers be: $x, \, x+2, \, x+4$ where $x$ is the smallest even integer.

Step 2: Write the equation for their sum

The sum of the three integers is given as $18$. Therefore, we write: $x + (x+2) + (x+4) = 18$

Step 3: Simplify the equation

Combine like terms: $3x + 6 = 18$

Step 4: Solve for $x$

Subtract $6$ from both sides: $3x = 12$ Divide by $3$: $x = 4$

Step 5: Find the integers

The integers are: $x = 4, \, x+2 = 6, \, x+4 = 8$

Final Answer:

The three consecutive even integers are: $4, \, 6, \, 8$

Would you like more explanation, or have questions?

Related Questions:

1. How do you solve for consecutive odd integers with a specific sum?
2. What happens if the sum of integers is negative?
3. Can consecutive integers include decimals?
4. How do we model the same problem with algebraic inequalities?
5. What are some real-world scenarios where similar equations are used?

Tip:

When solving problems with consecutive integers, always define variables clearly and check your work by substituting your solution back into the original equation!