Perimeter: \(2(w + 3w) = 8w = 160\) → \(w = 20\).

["Master Perimeter Calculation: Solving (2(w + 3w) = 8w = 160) Step-by-Step", "Understanding perimeter calculations is a fundamental math skill used in geometry, construction, architecture, and everyday problem-solving. One common problem involves simplifying expressions and solving for variables, such as in the equation:\n(2(w + 3w) = 8w = 160), leading to (w = 20).", "In this article, we break down how to solve this expression algebraically and explain why this method works—ideal for students, educators, and anyone looking to strengthen their algebraic skills.", "---", "### What Is the Perimeter in This Problem?", "In geometric terms, the perimeter is the total distance around a shape. Here, we’re working with a linear expression representing a perimeter or side measurement. The equation\n(2(w + 3w) = 160) models a scenario where a single segment repeated and doubled represents the total perimeter.", "---", "### Step-by-Step Breakdown of the Equation", "Start with the given expression:\n[ 2(w + 3w) = 160 ]", "Step 1: Simplify inside the parentheses\n[ w + 3w = 4w ]\nSo the equation becomes:\n[ 2(4w) = 160 ]", "Step 2: Multiply\n[ 8w = 160 ]\nThis simplifies the doubling and summation into a clean multiplication.", "Step 3: Solve for (w)\nDivide both sides by 8:\n[ w = \frac{160}{8} = 20 ]\nSo, the value of (w) is 20.", "---", "### Why This Problem Matters: Real-World Applications", "While abstract practice problems may seem robotic, similar perimeter calculations appear in:", "- Building construction: Estimating the length of material borders\n- Interior design: Planning room layouts or trim work\n- Gardening and landscaping: Calculating fence lengths\n- Manufacturing: Designing square or rectangular components", "Knowing how to simplify such equations quickly allows precise planning and resource estimation.", "---", "### How to Apply ExerciseIQ Principles", "At ExerciseIQ, we emphasize logical sequence and step mastery—so mastering perimeter problems builds foundational algebraic fluency. Practice often, verify each simplification, and recognize patterns early. This problem exemplifies how breaking complex expressions into simpler steps leads to accurate solutions.", "---", "### Final Summary", "Given:\n[ 2(w + 3w) = 8w = 160 ]\n[ 8w = 160 \Rightarrow w = 20 ]", "This simple equation demonstrates core algebraic techniques applied to perimeter contexts—combining, simplifying, and solving equations in one coherent flow.", "---", "### Pro Tips\n- Always simplify within parentheses first\n- Watch for repeated multiplication (e.g., (2(w + 3w) = 2 \cdot 4w))\n- Solve by inverse operations to isolate variables", "Master these habits, and you’ll confidently tackle more complex geometry and algebra problems.", "---", "Keywords: perimeter equation, solve linear equation, algebra practice, geometry problem solving, perimeter calculation tutorial, how to solve 2(w + 3w) = 160, step-by-step math, EXERCISE_IQ perimeter logic, simplify expressions algebraically.", "---", "For more math clarity and problem-solving strategies, visit our full geometry and algebra resources."]