Perimeter = \(2(w + 2w + 3) = 54\)

["# Solving the Perimeter Equation: (2(w + 2w + 3) = 54) – A Step-by-Step Guide", "When tackling geometry problems involving perimeters, understanding how to simplify and solve algebraic equations is key. One common equation you may encounter is:", "[\n2(w + 2w + 3) = 54\n]", "This equation represents the total perimeter of a shape (such as a rectangle) where (w) is the width and other dimensions depend on (w) in a defined way. In this article, we’ll break down how to solve this equation, interpret its meaning, and apply it practically.", "---", "## Understanding the Perimeter Equation", "The expression (w + 2w + 3) combines dimensions of a shape, typically representing a width ((w)), two widths ((2w)), and three constant units (perhaps side lengths or offsets). Multiplying by 2 yields the full perimeter.", "The goal is to solve for (w):", "[\n2(w + 2w + 3) = 54\n]", "---", "### Step-by-Step Solution", "Step 1: Simplify inside the parentheses", "Combine like terms:", "[\nw + 2w + 3 = 3w + 3\n]", "Now the equation is:", "[\n2(3w + 3) = 54\n]", "Step 2: Distribute the 2", "[\n2 \cdot 3w + 2 \cdot 3 = 6w + 6\n]", "So:", "[\n6w + 6 = 54\n]", "Step 3: Isolate the term with (w)", "Subtract 6 from both sides:", "[\n6w = 54 - 6 = 48\n]", "Step 4: Solve for (w)", "[\nw = \frac{48}{6} = 8\n]", "---", "## Final Answer", "The value of (w) that satisfies the equation is:", "[\n\boxed{w = 8}\n]", "---", "## What Does This Mean in Practical Terms?", "If (w = 8) represents a width in a geometric figure (such as a rectangular garden or room), plugging back in confirms:", "[\n2(w + 2w + 3) = 2(8 + 16 + 3) = 2(27) = 54\n]", "Which matches the given perimeter. Thus, knowing how to solve such equations helps in:", "- Determining unknown dimensions\n- Verifying design plans and architecture\n- Optimizing space usage in construction and interior design", "---", "## Summary", "Solving perimeter problems like (2(w + 2w + 3) = 54) involves simplifying expressions, applying algebraic operations, and isolating the variable. In this case:", "- Simplify: (w + 2w + 3 = 3w + 3)\n- Distribute: (2(3w + 3) = 6w + 6)\n- Solve: (6w + 6 = 54 \Rightarrow w = 8)", "By mastering step-by-step algebra, you can confidently solve realistic geometry problems involving perimeters.", "---", "## Key SEO Keywords", "- Solve perimeter equation\n- (2(w + 2w + 3) = 54) solution\n- Perimeter algebra step-by-step\n- How to find width from perimeter\n- Geometry problem solving\n- Algebraic perimeter calculation", "---", "Need more perimeter help? Whether it’s solving equations or applying geometry to real-world designs, mastering these fundamentals turns tough problems into simple tasks!"]