\[ 2(w + 2w) = 72 \] - Nurtured Nest
Solve the Equation 2(w + 2w) = 72: Step-by-Step Guide
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.
Understanding the Context
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.
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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
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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.
