How to Solve the Equation: 2(w + 2w) = 36 – A Step-by-Step Guide

Solving equations is a fundamental math skill that builds confidence in algebra. One common type of problem students encounter is simplifying expressions on one side of an equation and isolating the variable. In this article, we’ll walk through solving the equation:
2(w + 2w) = 36, step by step, while highlighting key algebraic techniques and problem-solving strategies for clarity and understanding.

Understanding the Context

Step 1: Simplify Inside the Parentheses

Start by simplifying the expression inside the parentheses:
w + 2w = 3w

So the equation becomes:
2(3w) = 36

> Tip: Combining like terms saves time and prevents errors later. Multiplying 2 by 3w directly gives 6w.

\[ 2(w + 2w) = 36 \]

Key Insights

Step 2: Simplify the Left Side

Now multiply:
2 × 3w = 6w

So the equation is simplified to:
6w = 36

Continue Reading

Since the panels are indistinguishable, no further labeling is needed. Therefore, the number of ways is $\boxed{25}$.
Question: A climatologist records daily rainfall anomalies over a 7-day period, each day’s anomaly being an integer from $0$ to $4$ mm, inclusive. How many sequences of anomalies are possible such that no two adjacent days have the same anomaly?
Solution: Each day has $5$ possible values: $0, 1, 2, 3, 4$.

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Final Thoughts

Step 3: Isolate the Variable

To find w, divide both sides by 6:
w = 36 ÷ 6
w = 6

Final Answer

✅ The solution is w = 6

Why This Equation Matters

Understanding how to solve equations like 2(w + 2w) = 36 is essential for developing algebraic fluency. This type of problem teaches key concepts such as:

  • Combining like terms
  • Distributive property
  • Isolating variables

Mastering these skills helps students tackle more complex equations and real-world modeling scenarios involving linear relationships.