المحيط هو \(2(w + 2w) = 6w = 50\)، إذن \(w = \frac{50}{6} \approx 8.33\).

["Solving the Equation: (2(w + 2w) = 6w = 50) and (w \approx 8.33)", "Understanding linear equations is fundamental in algebra, and solving them step-by-step builds confidence and clarity. A common equation encountered is (2(w + 2w) = 6w = 50). In this article, we’ll break down how to simplify this equation, solve for (w), and verify the result with a practical approximation.", "### The Equation: (2(w + 2w) = 50)", "Start with the original equation:\n[\n2(w + 2w) = 50\n]", "First, simplify the expression inside the parentheses:\n[\nw + 2w = 3w\n]\nSo the equation becomes:\n[\n2(3w) = 50\n]", "Next, multiply:\n[\n6w = 50\n]", "Now, isolate (w) by dividing both sides by 6:\n[\nw = \frac{50}{6}\n]", "### Simplifying the Value", "Simplify the fraction:\n[\nw = \frac{50}{6} = \frac{25}{3} \approx 8.33\n]", "Thus, the exact value is (\frac{25}{3}), but when approximated to two decimal places, (w \approx 8.33). This helps in real-world applications where whole or rounded numbers are needed.", "### Why This Equation Matters", "Equations like (2(w + 2w) = 50) often represent real-life scenarios—such as budgeting, distance calculations, or comparison problems—where scaling by a factor and solving for an unknown is essential. Such linear equations form the building blocks for more complex algebra.", "### Step-by-Step Summary", "1. Simplify inside the parentheses: (w + 2w = 3w)\n2. Multiply by 2: (2 \ imes 3w = 6w)\n3. Set equal to 50: (6w = 50)\n4. Divide both sides by 6: (w = \frac{50}{6} \approx 8.33)", "### Final Result", "[\n\boxed{w = \frac{25}{3} \approx 8.33}\n]", "Understanding how to solve this equation not only reinforces basic algebra skills but also prepares learners for tackling more advanced mathematical concepts. Whether for school, standardized tests, or daily problem-solving, mastering equation solving pays off.", "---", "Keywords: linear equations, solving for (w), algebra practice, (6w = 50), math tutorial, real-life equations, fraction simplification, exact vs approximate solutions\nMeta description: Learn how to solve (2(w + 2w) = 50) step by step, arriving at (w = \frac{25}{3} \approx 8.33)—perfect for algebra beginners."]