El perímetro es 2(x + 2x) = 60 cm, por lo que 6x = 60 cm.
["Solving the Linear Equation: El perímetro es 2(x + 2x) = 60 cm", "Understanding how to solve equations is fundamental in algebra, especially when dealing with real-world applications like geometry. One common problem students encounter is calculating the perimeter of a shape when given a linear expression for its side length. In this article, we’ll break down the equation El perímetro es 2(x + 2x) = 60 cm, simplify it to 6x = 60 cm, and explain how to solve for x step-by-step.", "---", "### Understanding the Problem", "In polygons such as rectangles, the perimeter is the total distance around the shape, calculated as the sum of all side lengths. When sides are expressed algebraically, simplifying the expression helps solve for unknown values.", "Here, we’re told the perimeter is represented as 2(x + 2x). Let’s interpret what this means:", "- The term (x + 2x) suggests one side has length x and an adjacent side (possibly twice as long) has length 2x.\n- Multiplying the entire perimeter expression by 2 accounts for both the length and width in a rectangle (like doubling the sum of two adjacent sides).\n- The result equals 60 cm, the total perimeter.", "---", "### Step-by-Step Simplification", "Start with the given equation:\n2(x + 2x) = 60 cm", "1. Combine like terms inside the parentheses:\n ( x + 2x = 3x )\n So, the equation becomes:\n2(3x) = 60 cm", "2. Multiply:\n ( 2 \ imes 3x = 6x )\n Now:\n6x = 60 cm", "This simplified equation, 6x = 60 cm, is easier to solve.", "---", "### Solving for x", "To isolate x, divide both sides by 6:\n[\nx = \frac{60}{6} = 10 \ ext{ cm}\n]", "Thus, x = 10 cm.", "---", "### Verifying the Solution", "Now that we know x, substitute it back into the original expression to ensure correctness:\n- One side: x = 10 cm\n- Other side: 2x = 20 cm\n- Perimeter: 2 × (10 + 20) = 2 × 30 = 60 cm, which matches the given value.", "---", "### Real-World Application", "This type of equation models scenarios such as framing a rectangular garden where one dimension depends linearly on another. Knowing the perimeter helps with material estimation—like fencing, flooring, or paint—making algebraic modeling a valuable skill in everyday situations.", "---", "### Conclusion", "The expression El perímetro es 2(x + 2x) = 60 cm is a classic example of translating geometric relationships into algebraic equations. Simplifying to 6x = 60 cm and solving for x reveals the missing dimension. Mastering such problems strengthens problem-solving abilities crucial in STEM fields and practical daily tasks.", "Key takeaways:\n- Combine like terms carefully before solving.\n- Always simplify coefficient expressions.\n- Verify results by plugging back into original equations.", "This equation exemplifies how elementary algebra underpins accurate real-world measurements and calculations.", "---", "Keywords for SE optimize article:\nEl perímetro es 2(x + 2x) = 60 cm, resolver ecuaciones lineales, cálculo de perímetro algebraico, resolver 2(x + 2x) = 60, ecuación 6x = 60, geometría algebraica, solución paso a paso ecuación lineal, aplicación práctica álgebra, cálculo de dimensiones geométricas."]
