Entonces, 2(4w) = 48 cm => 8w = 48 cm.

["Understanding 2(4w) = 48 cm: Solving for the Width (w) in Centimeters", "When solving equations involving geometry, especially in scenarios related to length, width, and perimeter, clarity and accuracy are key. One common problem students and learners encounter is equations like Entonces, 2(4w) = 48 cm ⇒ 8w = 48 cm. But what does this equation mean, and how do we properly solve it?", "### Breaking Down the Equation: 2(4w) = 48 cm", "In practical terms, this equation might describe a situation where a rectangular shape’s dimensions relate to a total perimeter measure. Let’s unpack the equation:", "- 2(4w): This represents twice the product of 4 times the width (w). In geometry, 4w is often the total length around one side (e.g., the perimeter of a rectangle if w is one side and 4 seems involved via a measurement or repetition).\n- = 48 cm: Sets the total linear dimension of interest to 48 centimeters.", "The multiplication inside the parentheses simplifies to:\n[\n2 \ imes 4w = 8w\n]\nSo the equation becomes:\n[\n8w = 48 , \ ext{cm}\n]", "This now clearly states that eight times the width (w) equals 48 centimeters.", "### Step-by-Step Solution", "To find the value of w, we solve the equation:\n[\n8w = 48 , \ ext{cm}\n]", "1. Divide both sides by 8 to isolate w:\n$$\nw = \frac{48}{8} , \ ext{cm}\n$$", "2. Simplify:\n$$\nw = 6 , \ ext{cm}\n$$", "Thus, the width w measures 6 centimeters.", "### Why This Matters in Real-World Applications", "Equations like 2(4w) = 48 cm often model real-world problems such as:\n- Calculating the width of a rectangular garden when the total perimeter (inoside measurements) and side ratios are known.\n- Solving layout or construction challenges where dimensions must conform to fixed measurements.", "Understanding how to simplify and solve such expressions ensures accurate design and calculations in architecture, carpentry, landscaping, and more.", "### Summary", "- Simplify expressions inside parentheses first: 2(4w) → 8w.\n- Rewrite the full equation clearly: 8w = 48 cm.\n- Solve by dividing both sides by 8: w = 48 ÷ 8 = 6 cm.\n- Verify units: Ensure your answer matches the original measure (cm).", "This straightforward algebraic process lays the foundation for more complex geometry and measurement problems — making it essential for math learners, educators, and professionals alike.", "---", "Key Takeaway:\nWhen solving 2(4w) = 48 cm, the correct simplification is 8w = 48 cm, leading to w = 6 cm. Mastering such steps enhances problem-solving accuracy in real-world mathematical applications."]