\[ 2(w + 2w) = 36 \] - United Radiology

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.

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.

Step 2: Simplify the Left Side

Now multiply:
2 × 3w = 6w

So the equation is simplified to:
6w = 36

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.

Practice Problem

Want to test yourself? Try solving:
3(2x + 4) = 24

Try simplifying, isolating, and solving just like above — you’ll end up with x = 2, reinforcing your understanding step by step.

Key Takeaways

• Always simplify expressions inside parentheses first.
  
• Use the distributive property to multiply coefficients.
  
• Balance the equation by performing the same operation on both sides.
  
• Solve step-by-step to avoid mistakes.

References & Further Reading

• Algebra for Beginners: Simplifying Expressions
  
• Mastering Linear Equations for Success in Math
  
• Online Algebra Practice Worksheet Tools

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2(w + 2w) = 36, solving linear equations, algebra steps, algebraic equation solving, simplify expressions, isolate variable, math tutorial, middle school algebra, school math practice

Check back often for more clear explanations on solving equations, word problems, and algebra basics!