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

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v=A: neighbors B → deg 1 → only A-B ∈ E → only one → no.
v=D: neighbors E → deg 1 → only DE → one → no.
v=C: deg 1, neighbors B → but BC ∈ E, but no other edge? Wait — in this setup, edges are AB, BC, DE — so C only connected to B → only one edge → deg 1.

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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.