["Solving 64 = 2(3w + w): A Step-by-Step Explanation", "If you’ve ever come across the equation 64 = 2(3w + w), you’re not alone. Whether you're a student learning algebra or someone looking to refresh your math skills, understanding how to solve this equation is essential. In this article, we’ll break down the solution step-by-step, explain the formula, and highlight how this equation appears in real-world problems.", "---", "### Understanding the Equation: 64 = 2(3w + w)", "The expression 64 = 2(3w + w) involves variables, parentheses, and basic arithmetic operations. Let’s decode it.", "- The left side, 64, is a constant number.
\n- The right side includes:
\n - Inside parentheses: 3w + w, which combines two instances of the variable w.
\n - Multiplied by 2: indicating scaling.", "This structure is common in real-life applications—especially when modeling linear relationships.", "---", "### Step-by-Step Solution", "#### Step 1: Simplify Inside the Parentheses", "Start by simplifying the expression inside the parentheses:
\n\[ 3w + w = 4w \]", "So the equation becomes:
\n\[ 64 = 2(4w) \]", "#### Step 2: Multiply Both Sides by 2", "Since 2 is multiplied by \(4w\), multiply both sides of the equation by 1 (effectively leaving the multiplication) to simplify:
\n\[ 64 = 8w \]", "> Why multiply both sides?
\nTo isolate the variable w, we must first simplify the expression on the right side.", "#### Step 3: Solve for w", "Now divide both sides by 8:
\n\[ w = \frac{64}{8} \]
\n\[ w = 8 \]", "---", "### Verifying the Solution", "Plug \(w = 8\) back into the original equation:
\n\[ 2(3(8) + 8) = 2(24 + 8) = 2(32) = 64 \]
\n✅ The equation holds true.", "---", "### Real-World Applications of This Equation", "Equations like 64 = 2(3w + w) often appear in:", "- Business and Economics: When calculating costs, revenue, or break-even points where multiple fixed and variable terms interact.
\n- Physics: Modeling motion with linear relationships involving distance, speed, and time.
\n- Design and Engineering: Balancing material usage, dimensions, and constraints in projects.", "Understanding how to solve such equations empowers you to work confidently with linear relationships in technical and everyday scenarios.", "---", "### Summary", "- Start by simplifying expressions inside parentheses.
\n- Apply basic algebra: divide both sides by coefficients to isolate the variable.
\n- Always substitute back to verify.", "Final Answer:
\n\[
\n\boxed{w = 8}
\n\]", "---", "### Why You Should Know This", "Mastering basic algebra equations strengthens your problem-solving foundation. Techniques used here—simplification, multiplication, and isolation of variables—are tools you’ll reuse daily in academics and professional life.", "---", "Meta Keywords:
\n64 = 2(3w + w), solve linear equation, algebra tutoring, how to solve equations, algebra step-by-step, math problem solver, w = ?, linear equation solution", "Tags:

Algebra #MathTips #EquationSolving #WEquals8 #LinearEquations #STEMEducation", "---", "If you found this guide helpful, share it to help others master algebra basics. Stay tuned for more clear, actionable math explanations!"]