Perimeter: \( 2(w + 3w) = 40 \) → \( 8w = 40 \) → \( w = 5 \).
["Solving the Simple Linear Equation: Perimeter and Width — Explained Step-by-Step", "Understanding basic algebra is essential for solving everyday math problems. One common equation you may encounter involves the perimeter of a rectangle, especially when expressions for dimensions are included. Let’s break down the equation ( 2(w + 3w) = 40 ) and solve it step-by-step to find the value of ( w ).", "---", "### Understanding the Problem", "The perimeter of a rectangle is calculated using the formula:\n[\n\ ext{Perimeter} = 2 \ imes (\ ext{length} + \ ext{width})\n]", "In this problem, the equation ( 2(w + 3w) = 40 ) represents a perimeter scenario where:\n- ( w ) is the width,\n- ( 3w ) is the length — possibly 3 times the width —\n- The total perimeter equals 40 units.", "---", "### Step 1: Simplify the Expression Inside the Parentheses", "Start by simplifying ( w + 3w ):\n[\nw + 3w = 4w\n]\nSo the original equation becomes:\n[\n2(4w) = 40\n]", "---", "### Step 2: Multiply to Eliminate the Parentheses", "Multiply ( 2 \ imes 4w ):\n[\n8w = 40\n]", "---", "### Step 3: Solve for ( w )", "Now divide both sides by 8 to isolate ( w ):\n[\nw = \frac{40}{8} = 5\n]", "---", "### Final Answer", "The width of the rectangle is:\n[\n\boxed{5}\n]", "---", "### Why This Matters", "Solving equations like ( 2(w + 3w) = 40 ) helps you model real-world scenarios, such as designing a garden, planning a room renovation, or calculating material needs. Mastering such algebra builds a strong foundation for more complex math and practical problem-solving.", "---", "### Key Takeaways", "- Simplify expressions inside parentheses first.\n- Apply multiplication rules to clear parentheses.\n- Use division to solve for the variable.\n- Always verify your solution by plugging back into the original equation.", "---", "Practice Tip: Try replacing ( w = 5 ) into the original equation to confirm:\n[\n2(5 + 15) = 2 \ imes 20 = 40 \quad \ ext{(True!)}\n]", "---", "Keywords: perimeter equation, algebraic equation, solving for ( w ), linear equation, math tutorial, elementary algebra, step-by-step solution, word problem math", "---", "If you're learning algebra or teaching students, solving ( 2(w + 3w) = 40 ) offers a clear and engaging example of perimeter and equation solving. Make it interactive with real-life applications — your understanding (and test scores) will improve!"]
