Perimeter equation: \( 2(w + 3w) = 64 \).

["Understanding the Perimeter Equation: How to Solve ( 2(w + 3w) = 64 )", "The perimeter equation ( 2(w + 3w) = 64 ) is a classic algebra problem that helps students and learners practice simplifying expressions and solving linear equations. Whether you're a student solving homework or a teacher explaining foundational math concepts, understanding how to approach this equation builds strong problem-solving skills. In this SEO-optimized article, we break down the perimeter equation step-by-step, explain its real-world applications, and guide you through solving it efficiently.", "---", "### What is a Perimeter Equation?", "A perimeter equation relates numerical expressions to the total length around a shape, often involving variables. In this case, ( 2(w + 3w) = 64 ), represents the perimeter of a rectangle where the width is ( w ) and one length side is ( 3w ). The equation sets the total perimeter equal to 64 units.", "---", "### Why Learn and Solve Perimeter Equations?", "Solving perimeter equations strengthens your algebraic foundation by:", "- Simplifying linear expressions,\n- Combining like terms,\n- Isolating variables,\n- Applying algebra to geometric real-world problems.", "This equation is especially common in basic geometry and algebra lessons, making it valuable for standardized test prep and everyday math application.", "---", "### Step-by-Step Guide to Solving ( 2(w + 3w) = 64 )", "Step 1: Simplify inside the parentheses\nThe expression ( w + 3w ) combines to ( 4w ):\n[ 2(w + 3w) = 2(4w) = 8w ]", "Step 2: Rewrite the equation\nSubstitute back into the original equation:\n[ 8w = 64 ]", "Step 3: Isolate the variable\nDivide both sides by 8:\n[ w = 64 \div 8 = 8 ]", "---", "### What does the solution mean?", "Since ( w = 8 ), the width is 8 units. The longer side is ( 3w = 3 \ imes 8 = 24 ) units.\nCalculating the perimeter:\n[ 2(8 + 24) = 2(32) = 64 ]\nWhich matches the given total — confirming the solution is correct.", "---", "### Real-World Applications", "Perimeter equations like ( 2(w + 3w) = 64 ) appear in:", "- Interior design: Calculating dimensions for rectangular rooms or crown moldings\n- Construction & carpentry: Estimating material lengths for framing\n- Gardening: Planning flower bed borders or fencing projects\n- Education: Teaching proportional reasoning and algebraic thinking", "---", "### Tips to Solve Similar Equations", "- Always simplify expressions inside parentheses first.\n- Combine like terms before isolating the variable.\n- Use inverse operations to solve for unknowns.\n- Always substitute the solution back to verify correctness.", "---", "### Final Answer", "The solution to the perimeter equation ( 2(w + 3w) = 64 ) is:\nWidth = 8 units, Length = 24 units.\nThis yields a correct perimeter of 64 units.", "---", "### SEO Keywords for Optimization", "- Perimeter equation solution\n- Solve ( 2(w + 3w) = 64 )\n- Algebra perimeter problems\n- Intermediate algebra equations\n- Step-by-step solving perimeter\n- Real-world math applications\n- Teach algebra through perimeter", "---", "### Conclusion", "Mastering the perimeter equation ( 2(w + 3w) = 64 ) enhances algebraic fluency and problem-solving. By simplifying step-by-step and verifying results, learners gain confidence in handling similar equations. Whether applying geometry in daily life or advancing in math, understanding how to solve such equations is essential.", "---", "Need more algebra practice? Explore our guides on other linear equations, quadratic perimeter problems, and real-world math applications to sharpen your skills!", "---", "Keywords for search: perimeter equation, solve 2(w + 3w) = 64, linear equations algebra, intermediate algebra practice, geometry and algebra fusion\nRelated topics: Perimeter formulas for rectangles and squares, Algebraic word problems, Solving equations with variables on both sides."]