Solving 2(2w + w) = 36: A Simple Step-by-Step Guide for Beginners

Understanding how to solve equations is a fundamental skill in algebra, and equation like 2(2w + w) = 36 is one of the most common beginners’ problems. In this article, we’ll walk you through solving this equation step-by-step, explain the key algebraic principles, and show how this method applies to real-world problem-solving.

Understanding the Context

What Does the Equation Mean?

The equation 2(2w + w) = 36 represents a real-life scenario where two times the sum of 2w and w equals 36. Breaking it down:

  • Inside the parentheses: 2w + w — combining like terms means w adds to 2w, giving 3w
  • Then multiplied by 2: 2 × 3w = 6w

So the equation simplifies to:
6w = 36

2(2w + w) = 36

Key Insights

Step-by-Step Solution

Step 1: Simplify the expression inside the parentheses
Start with the original equation:
2(2w + w) = 36

Since 2w + w = 3w, replace it:
2 × 3w = 36

Multiply:
6w = 36

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Final Thoughts

Step 2: Isolate the variable w
To solve for w, divide both sides of the equation by 6:
6w ÷ 6 = 36 ÷ 6

This gives:
w = 6

Verifying the Solution

Plug w = 6 back into the original equation:
2(2×6 + 6) = 2(12 + 6) = 2×18 = 36 ✔️

The solution checks out!

Why Understanding This Matters

Solving 2(2w + w) = 36 isn’t just about finding w = 6—it’s about mastering essential algebraic tools:

  • Combining like terms: Combining 2w and w simplifies expressions for easier solving.
  • Distributing multiplication over addition: Applying the 2 to each term inside the parentheses correctly ensures accuracy.
  • Isolating variables: Dividing both sides to find the unknown variable is a core technique in any equation-solving scenario.