n + ( n  +  2 )  +  ( n  +  4 ) = 84 if x=26

The equation given is \( n + (n + 2) + (n + 4) = 84 \).

However, the variable \( x = 26 \) is provided, which suggests there might be confusion between \( n \) and \( x \). Since the equation involves \( n \), we should clarify if you meant to ask about solving for \( n \) or substituting \( x = 26 \).

### Scenario 1: Solving for \( n \)
If you want to solve the equation for \( n \):

1. **Simplify the equation:**

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

   Combine like terms:

   \[
   3n + 6 = 84
   \]

2. **Isolate \( n \):**

   Subtract 6 from both sides:

   \[
   3n = 78
   \]

   Divide by 3:

   \[
   n = 26
   \]

So, \( n = 26 \).

### Scenario 2: Checking if \( x = 26 \) works in place of \( n \)
If you want to check if substituting \( x = 26 \) into \( n + (n + 2) + (n + 4) = 84 \) satisfies the equation:

1. **Substitute \( n = 26 \):**

   \[
   26 + (26 + 2) + (26 + 4) = 84
   \]

2. **Simplify:**

   \[
   26 + 28 + 30 = 84
   \]

   \[
   84 = 84
   \]

This confirms that \( n = 26 \) is indeed the correct solution.

Would you like further details or have any questions?

---

Here are five related questions:

1. How can we solve equations with multiple variables?
2. What does it mean to substitute a value into an equation?
3. How do you check if a given number satisfies an equation?
4. How can we derive equations for consecutive numbers?
5. What are some common mistakes to avoid when simplifying algebraic expressions?

**Tip:** When solving equations, it's essential to combine like terms and simplify the equation step by step to avoid errors.

Explore how to solve equations involving multiple variables and understand the process of substitution in algebraic equations. This detailed guide covers key concepts in algebra and equation simplification. Suitable for Grades 7-9 students and anyone interested in mastering algebraic problem-solving techniques.

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