\[ 2(w + 2w) = 72 \] - Project Allmight

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.

Learn More with Related Keywords

Optimize your learning with these relevant SEO keywords and phrases:
- Solve linear equations algebra
- How to simplify expressions step-by-step
- Algebraic equations for beginners
- Step-by-step equation solving guide
- Linear equations practice problems

Use these terms in blog titles, meta descriptions, and headings to boost your article’s search engine visibility.

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.