2(w + 2w) = 36 \implies 6w = 36 \implies w = 6 - Groen Casting
Understanding the Equation: 2(w + 2w) = 36 Implies 6w = 36 → w = 6
Understanding the Equation: 2(w + 2w) = 36 Implies 6w = 36 → w = 6
Solving linear equations step-by-step is a fundamental skill in algebra, essential for students, educators, and anyone working with mathematical reasoning. One common example is the equation 2(w + 2w) = 36. This equation appears simple but serves as a perfect teaching example to demonstrate how algebraic manipulation leads to a solution.
Breaking Down the Equation
Start with the original equation:
2(w + 2w) = 36
Understanding the Context
First, simplify inside the parentheses. Combine like terms—here, w and 2w:
w + 2w = 3w
So the equation becomes:
2(3w) = 36
Now apply multiplication:
6w = 36
This transformation reflects the distributive property — multiplying 2 by 3w gives 6w.
Solving for w
To isolate w, divide both sides by 6:
6w ÷ 6 = 36 ÷ 6
w = 6
Why This Equation Matters
Understanding how to simplify and solve equations like 2(w + 2w) = 36 builds strong algebraic intuition. This step-by-step approach helps recognize patterns, apply properties of equality (like division or multiplication over both sides), and confirm solutions — all crucial skills for advanced math topics including functions, systems of equations, and real-world problem-solving.
Key Insights
Key Takeaways
- Combine like terms early to simplify expressions.
- Apply distributive property when multiplying across parentheses.
- Use inverse operations to isolate variables.
- Always verify solutions by substituting back into the original equation.
Whether you're a student mastering algebra or a parent supporting learning at home, mastering equations like 2(w + 2w) = 36 strengthens foundational math skills. Practice with similar equations daily to grow confidence and fluency in solving linear expressions.
