The perimeter is given by \(2(x + 2x) = 6x = 72\).

["# How to Solve “The Perimeter is Given by (2(x + 2x) = 6x = 72)”: A Step-by-Step Guide", "Understanding how to solve linear equations like (2(x + 2x) = 6x = 72) is essential for mastering algebra. Whether you're a student tackling homework or simply enhancing your math skills, knowing how to interpret and solve perimeter-related expressions can simplify complex word problems. In this article, we break down the solution step-by-step and explain how to apply this method to any problem involving linear equations derived from real-world geometry.", "## Understanding the Perimeter Equation", "Perimeters quantify the total distance around a two-dimensional shape. In many problems, the perimeter of a rectangle is given using a formula like (2(\ ext{length} + \ ext{width})). When simplified, this becomes (2(x + 2x) = 6x), where (x) represents a linear dimension such as a side length.", "Here, the equation (6x = 72) states that doubling the sum of the length and width results in a perimeter of 72 units.", "## Simplifying the Expression", "Start with:\n[\n2(x + 2x)\n]\nCombine like terms inside the parentheses:\n[\nx + 2x = 3x\n]\nSo, the perimeter formula simplifies to:\n[\n2(3x) = 6x\n]", "Thus, the original equation becomes:\n[\n6x = 72\n]", "## Solving for (x)", "To isolate (x), divide both sides of the equation by 6:\n[\nx = \frac{72}{6} = 12\n]", "So, (x = 12). This value defines the scaling factor used in the dimensions.", "## Interpreting the Solution", "Since (x = 12), the width of the rectangle is (x = 12) units, and the length is (2x = 24) units. The perimeter checks out:\n[\n2(12 + 24) = 2(36) = 72\n]\nwhich confirms the solution is correct.", "## Why This Method Matters", "Solving equations like (2(x + 2x) = 6x = 72) is a foundation for tackling real-life perimeter and area problems. Whether designing a garden, calculating materials, or planning spaces, algebraic perimeter equations help model and solve geometric challenges efficiently.", "## How to Apply This Approach", "1. Simplify the expression inside the parentheses. Combine like terms to reduce the equation.\n2. Distribute any coefficients to eliminate parentheses.\n3. Isolate the variable by applying inverse operations.\n4. Solve for the unknown and verify by substituting back into the original equation.", "## Summary", "The equation (2(x + 2x) = 6x = 72) simplifies directly to (6x = 72), leading to (x = 12), a critical step in determining side lengths and overall perimeter. Mastering this method empowers you to solve a wide range of problems involving linear dimensions and perimeters in both academic and practical settings.", "Next time you encounter a perimeter problem expressed algebraically, recall how simplifying and solving step-by-step provides clear, accurate answers. Practice recognizing such patterns, and you’ll build confidence in algebra and geometry!", "---", "Keywords: perimeter equation, solve 2(x + 2x) = 6x = 72, algebra for beginners, linear equations, geometry problem-solving, step-by-step perimeter solution, simplify expressions, algebra tutorial, x = 12, geometry and algebra.", "---", "If you found this guide helpful, stay tuned for more step-by-step math lessons — from perimeters to quadratics!"]