Perimeter: \( 2(w + 2w) = 48 \Rightarrow 6w = 48 \Rightarrow w = 8 \).

["# Mastering Linear Equations: A Step-by-Step Guide to Solving ( 2(w + 2w) = 48 )", "Solving linear equations is a foundational skill in algebra that opens the door to understanding more complex mathematical concepts. One common equation students encounter is ( 2(w + 2w) = 48 ). This seemingly simple equation serves as an excellent example of how to simplify expressions, combine like terms, and isolate variables step-by-step. In this article, we’ll break down how to solve ( 2(w + 2w) = 48 ), explain each step thoroughly, and demonstrate its real-world relevance. Whether you're a student, educator, or lifelong learner, mastering this process will strengthen your problem-solving toolkit.", "## Understanding the Equation", "The equation ( 2(w + 2w) = 48 ) involves a linear expression with a variable ( w ). Without simplifying inside the parentheses first, solving the equation becomes unnecessarily complicated. Let’s begin by simplifying the expression within the parentheses.", "### Step 1: Combine Like Terms", "Inside the parentheses, ( w + 2w ) represents the sum of ( w ) and twice ( w ). Combining these gives:", "[\nw + 2w = 3w\n]", "Substituting back, the equation becomes:", "[\n2(3w) = 48\n]", "Notice how combining like terms simplifies the left-hand side significantly, making the next steps easier.", "### Step 2: Multiply Inside the Parentheses", "Now multiply the constant ( 2 ) by ( 3w ):", "[\n2 \ imes 3w = 6w\n]", "So the equation reduces to:", "[\n6w = 48\n]", "This step transforms the originally nested expression into a straightforward multiple of ( w ), setting us up for isolation of the variable.", "### Step 3: Isolate the Variable", "To solve for ( w ), divide both sides of the equation by 6:", "[\nw = \frac{48}{6} = 8\n]", "Thus, the solution is ( w = 8 ), a clean and precise value satisfying the original equation.", "## Why This Matters: Real-World Application", "Equations like ( 2(w + 2w) = 48 ) represent real-life scenarios where quantities grow linearly. For example, imagine buying two identical items, each priced at ( w ) dollars, and including twice that amount for wrapping and tax. The total cost being $48 leads directly to this equation. Solving it confirms that each item costs $8, demonstrating how algebra grounds everyday decisions.", "## Summary of the Solution Process", "We began with:", "[\n2(w + 2w) = 48\n]", "1. Simplified inside parentheses: ( w + 2w = 3w )\n2. Multiplied by 2: ( 2 \ imes 3w = 6w )\n3. Divided both sides by 6: ( w = 8 )", "Thus, ( w = 8 ) is the solution.", "## Final Thoughts", "Understanding how to solve ( 2(w + 2w) = 48 ) illustrates the power and elegance of algebraic simplification. By systematically combining like terms and isolating the variable, you transform complexity into clarity. This approach lays the foundation for tackling more advanced math. Keep practicing—each equation solved is a step toward mathematical mastery.", "---", "Keywords:\nlinear equation solving, algebra basics, how to solve 2(w + 2w) = 48, step-by-step algebra, variable substitution, simplify expressions, solve for w, algebra tutorial, mathematical methods, equation solving techniques.", "Meta Description:\nLearn how to solve ( 2(w + 2w) = 48 ) step-by-step. This comprehensive guide explains simplifying expressions, combining like terms, and isolating variables—essential skills for mastering algebra and real-world problem-solving."]