\[ 2(w + 2w) = 36 \] - Imagemakers
How to Solve the Equation: 2(w + 2w) = 36 – A Step-by-Step Guide
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.
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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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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.
