Le périmètre est donné par : \( 2(x + 2x) = 60 \).
["Title: Solving Linear Equations: Understanding the Perimeter Formula\nMeta Description: Learn how to solve the equation ( 2(x + 2x) = 60 ) step-by-step. This simple algebra problem explores the concept of perimeter in linear form—perfect for students and math enthusiasts.", "---", "### Solving Le Périmètre : Un Énoncé en Algèbre Simples ( 2(x + 2x) = 60 )", "When we talk about le périmètre in geometry, we refer to the total distance around a shape—often a simple closed figure like a rectangle. But what if the perimeter is described in algebraic terms? Consider this equation:", "[\n2(x + 2x) = 60\n]", "At first glance, this looks like a straightforward algebraic expression—but it’s also a practical model for finding unknown lengths tied to perimeter. Let’s break it down clearly and step-by-step.", "---", "### Step 1: Simplify the Expression Inside the Parentheses", "The key to solving ( 2(x + 2x) = 60 ) starts with simplifying the term inside the parentheses.", "[\nx + 2x = 3x\n]", "So the equation becomes:\n[\n2(3x) = 60\n]", "Multiplication of scalar coefficients is direct:\n[\n6x = 60\n]", "---", "### Step 2: Isolate the Variable ( x )", "To solve for ( x ), divide both sides of the equation by 6:\n[\nx = \frac{60}{6} = 10\n]", "This tells us that the unknown length ( x ), representing one segment of the perimeter portion, equals 10 units.", "---", "### Step 3: Understand the Real-World Application—Perimeter Simplified", "In real-life applications, this equation could model a problem where a shape—say a rectangle—has sides related through the given formula. For example, if the perimeter depends on a linear combination of length and width, such as ( 2(\ ext{width} + 2 \ imes \ ext{length}) ), solving this expression helps determine individual dimensions or the total perimeter.", "Here, since ( x = 10 ), this alone suggests a fundamental segment of the shape’s perimeter. Combined with proper geometric interpretation, this algebraic solution gives actionable insight.", "---", "### Final Calculation", "We already solved:\n[\n6x = 60 \Rightarrow x = 10\n]", "Thus, the value of ( x )—representing one piece of the geometric perimeter—is:\n[\n\boxed{10}\n]", "---", "### Conclusion: Solving Perimeter Problems with Algebra", "Understanding how expressions like ( 2(x + 2x) = 60 ) translate into real-world dimensions demystifies perimeter calculations. This algebraic method is fundamental not just for solving equations, but for applying math to architecture, construction, design, and more.", "Keywords: périmètre, solve linear equation, algebra 101, perimeter formula, ( 2(x + 2x) = 60 ), step-by-step math, equation solving, geometry application, solve for x, algebraic expressions.", "---", "Ready to tackle more math problems? Start simplifying expressions, isolate variables, and connect algebra to geometry today!"]
