Entonces, \( 2(3w + w) = 64 \).
["# Solving the Equation: Entonces, ( 2(3w + w) = 64 )", "### Understanding the Equation Step by Step", "In algebra, solving equations like ( 2(3w + w) = 64 ) is a foundational skill that helps you find the value of the unknown variable ( w ). Let’s break down this equation clearly using the Expanded Distributive Property and Combining Like Terms, starting with the simplified form that answers the question: what is ( w )?", "---", "## Step 1: Expand Inside the Parentheses", "The expression inside the parentheses is ( 3w + w ). Combine like terms:", "[\n3w + w = 4w\n]", "So the equation becomes:", "[\n2(4w) = 64\n]", "---", "## Step 2: Simplify the Multiplication", "Multiply ( 2 \ imes 4w ):", "[\n8w = 64\n]", "---", "## Step 3: Solve for ( w )", "To isolate ( w ), divide both sides of the equation by 8:", "[\nw = \frac{64}{8} = 8\n]", "---", "## Final Answer: ( w = 8 )", "Plugging ( w = 8 ) back into the original equation confirms correctness:", "[\n2(3 \cdot 8 + 8) = 2(24 + 8) = 2 \cdot 32 = 64\n]", "✅ The equation holds true — this validates our solution.", "---", "## Why Learning This Matters", "Solving linear equations like ( 2(3w + w) = 64 ) builds critical thinking and algebraic fluency. It helps in real-world scenarios such as:", "- Calculating expenses or projected growth\n- Modeling linear relationships in science and finance\n- Developing step-by-step reasoning required in programming and data analysis", "Understanding how to compute and verify solutions strengthens your problem-solving toolkit in mathematics and beyond.", "---", "## Summary\nThe equation ( 2(3w + w) = 64 ) simplifies step-by-step to find:", "[\nw = 8\n]", "Mastering these basic steps paves the way for tackling more complex algebraic expressions and advanced mathematical challenges.", "---", "### FAQ: Common Questions About Solving ( 2(3w + w) = 64 )", "Q: Why do we distribute the 2?\nA: Parentheses group terms that must be combined before simplifying, and distributing ensures accurate arithmetic.", "Q: Can we solve this without expanding?\nA: Yes, by factoring: ( 2(4w) = 64 \Rightarrow 8w = 64 ). But expanding reinforces understanding.", "Q: What if it were ( 2(3w + w + 4) = 64 )?\nA: Combine inside the parentheses first: ( 2(4w + 4) = 64 ), then simplify to isolate ( w ).", "---", "Start solving equations with confidence—every step brings you closer to mastering algebra!"]
