\[ 2(w + 2w) = 72 \]
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Solve the Equation 2(w + 2w) = 72: Step-by-Step Guide
If you're tackling algebra, you’ve likely encountered expressions like 2(w + 2w) = 72. This equation is a common starting point for students learning to simplify expressions and solve linear equations. In this SEO-optimized article, we’ll explore how to solve 2(w + 2w) = 72 step-by-step, explain the logic behind each step, and offer tips to master similar problems.
What is the Equation 2(w + 2w) = 72 All About?
The equation 2(w + 2w) = 72 involves simplifying a linear expression inside parentheses and solving for the unknown variable w. It’s a great example of combining like terms and applying basic algebraic operations.
Why solve equations like this?Solving linear equations strengthens foundational algebra skills, prepares students for more advanced math, and appears frequently on standardized tests and school assessments.
Step-by-Step Solution
Step 1: Combine like terms inside the parentheses
Inside the parentheses, w + 2w:- Both terms involve w, so add the coefficients: \( 1w + 2w = 3w \)
Now rewrite the equation:\[2(3w) = 72\]
Step 2: Multiply the constants
Multiply 2 by 3w:\[6w = 72\]
Step 3: Isolate the variable
Divide both sides by 6 to solve for w:\[w = \frac{72}{6} = 12\]
✅ Final Answer
\[\boxed{w = 12}\]
How to Check the Answer
Pull w = 12 back into the original equation to verify:\[2(12 + 2 \cdot 12) = 2(12 + 24) = 2(36) = 72\]✔️ The equation holds true.
Practical Applications
Understanding how to solve simple linear equations like 2(w + 2w) = 72 teaches problem-solving basics. You’ll use similar logic when:
- Calculating per-unit prices or total costs- Determining time, distance, or rate relationships- Analyzing data trends in science and economics
Key Takeaways
- Simplify first: Combine like terms inside parentheses.- Multiply mentely: Apply coefficients outside parentheses carefully.- Isolate variables: Use inverse operations to solve for unknowns.- Check your work: Substitute the solution back into the original equation.
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Conclusion
Mastering equations like 2(w + 2w) = 72 builds confidence in algebra and opens the door to advanced math topics. Whether you're a student, teacher, or self-learner, practicing step-by-step simplification and solution ensures success. Keep practicing by using similar expressions and expanding your algebraic toolkit!
Ready for more? Try solving 3(2w + w) = 75 or explore how to factor and solve equations like quadratic types, all while boosting your math skills through clear, practical steps.
