Perimeter is \( 2(x + 3x) = 64 \); solving gives \( 8x = 64 \), so \( x = 8 \).
["Solve the Equation: Perimeter ( 2(x + 3x) = 64 ) – Step-by-Step Solution\nMaster solving linear equations with real-world context and clear examples", "Understanding how to solve basic algebraic equations is essential for students and math enthusiasts alike. One everyday application appears when calculating the perimeter of rectangular shapes, especially when side relationships are expressed algebraically. Today, we explore the equation Perimeter = ( 2(x + 3x) = 64 ), walk through its solution step by step, and discover how such problems connect to geometry in real life.", "---", "### What is the Perimeter Equation?", "In geometry, the perimeter of a rectangle is calculated using the formula:\n[\n\ ext{Perimeter} = 2 \ imes (\ ext{Length} + \ ext{Width})\n]\nIn this problem, the width is defined as ( x ), and the length is ( 3x ) — meaning the length is three times the width. Substituting into the perimeter formula gives:\n[\n2(x + 3x) = 64\n]\nThis equation models a real-world scenario such as framing a rectangular garden where the total fencing required matches the perimeter expression.", "---", "### Step-by-Step Solution", "Let’s solve the equation algebraically:", "1. Simplify inside the parentheses\n[\nx + 3x = 4x\n]\nSo the equation becomes:\n[\n2(4x) = 64\n]", "2. Simplify the left-hand side:\n[\n8x = 64\n]", "3. Solve for ( x ) by dividing both sides by 8:\n[\nx = \frac{64}{8} = 8\n]", "---", "### Final Answer\nThe solution to the equation ( 2(x + 3x) = 64 ) is ( x = 8 ). This means the width is 8 units, and the length is ( 3x = 24 ) units, resulting in a perimeter of:\n[\n2(8 + 24) = 2 \ imes 32 = 64 \ ext{ units}\n]\nPerfectly matching the given condition.", "---", "### Why This Formula Matters", "Solving such equations connects abstract algebra with tangible applications in construction, interior design, and physics. Recognizing relationships like ordered side lengths (( 3x ) vs. ( x )) allows for efficient problem-solving in real-world planning and mathematical modeling.", "---", "### Practice Tip:\nTry substituting ( x = 8 ) back into the original equation:\n[\n2(8 + 3 \ imes 8) = 2(8 + 24) = 2 \ imes 32 = 64\n]\n✅ The equation holds—confirming your solution is accurate.", "---", "Mastering equations like ( 2(x + 3x) = 64 ) builds a strong foundation in algebra, critical for advanced math and STEM fields. Practice regularly to grow confidence and clarity!", "---", "Keywords: perimeter equation, solve linear equation, algebraic problem solving, geometry math, solve for x, math tutorial, basic algebra, quadratic methods simplified, real-world math applications"]
