["Title: Solve \( 2(3w + w) = 64 \): Step-by-Step Substitution and Easy Equation Solving", "Meta Description: Struggling with \( 2(3w + w) = 64 \)? Discover a clear, step-by-step substitution method to solve for \( w \), overcome algebra challenges, and boost your math confidence today!", "---", "Intro
\nAlgebra often feels overwhelming, but solving equations doesn’t have to be—especially with a little substitution strategy. One common type of equation to master is expressions involving parentheses and coefficients, like \( 2(3w + w) = 64 \). Whether you’re a student learning algebra or someone brushing up your math skills, understanding how to simplify and solve such equations is essential. This article breaks down the substitution approach for solving \( 2(3w + w) = 64 \), providing clear explanations and practical steps to get you through it with ease.", "---", "Understanding the Equation
\nThe equation \( 2(3w + w) = 64 \) combines parentheses, variable terms, and a multiplication factor. Let’s first understand what’s happening algebraically:", "- Inside the parentheses: \( 3w + w \) simplifies to \( 4w \), so the equation becomes \( 2(4w) = 64 \), or \( 8w = 64 \).
\n- But instead of skipping directly to simplifying, let’s explore a substitution method that strengthens your algebraic reasoning.", "---", "Step-by-Step Substitution Strategy
\nSubstitution in algebra means replacing an expression with a variable or simplified form to make solving easier. With \( 2(3w + w) = 64 \), here’s how substitution helps:", "1. Identify the repeated expression:
\n Notice \( 3w + w \) appears as a grouped term. Let’s define a substitution:
\n \[
\n x = 3w + w
\n \]
\n This simplifies our equation to:
\n \[
\n 2x = 64
\n \]", "2. Solve the substituted equation:
\n Divide both sides by 2:
\n \[
\n x = \frac{64}{2} = 32
\n \]", "3. Back-substitute to find \( w \):
\n Since \( x = 3w + w \), substitute \( x = 32 \):
\n \[
\n 3w + w = 32 \quad \Rightarrow \quad 4w = 32
\n \]
\n Divide both sides by 4:
\n \[
\n w = \frac{32}{4} = 8
\n \]", "---", "Why This Substitution Works
\nUsing substitution transforms a compound expression into a single variable, making the equation linear and straightforward to solve. It mirrors how advanced math uses variables to streamline problem-solving—this simple step builds foundational skills for tackling systems of equations and functions.", "---", "Final Answer
\nThe solution to \( 2(3w + w) = 64 \) is:
\n\[
\n\boxed{w = 8}
\n\]", "---", "Conclusion
\nSolving \( 2(3w + w) = 64 \) is simple once you break it down: substitute \( x = 3w + w \) to linearize the equation, solve step-by-step, and back-substitute. With consistent practice, algebraic substitution becomes second nature—boosting your problem-solving powers one equation at a time.", "Key SEO Keywords:

solve linear equations, algebra substitution method, solve \( 2(3w + w) = 64 \), step-by-step algebra, linear equations explained, equation simplification, w variable equation", "---", "Additional Tips:

\n
• Always simplify inside parentheses first.
\n
• Substitute to reduce complexity, especially in multi-term expressions.
\n
• Verify your answer by plugging \( w = 8 \) back into the original equation:
  \n \( 2(3(8) + 8) = 2(24 + 8) = 2(32) = 64 \) — correct!", "---", "Ready to master substitution? Try more equations like this and build algebra confidence today!"]
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