["# How to Solve (2(2w + w) = 48): Step-by-Step Guide", "Understanding how to solve simple linear equations is essential for mastering algebra. One commonly encountered problem is solving the equation:", "[
\n2(2w + w) = 48
\n]", "This article provides a clear, step-by-step solution to this equation, explains key algebraic concepts, and shows how such problems appear in real-world contexts. Whether you're a student, a teacher, or someone revisiting foundational math skills, this guide will help you solve this equation confidently and efficiently.", "---", "## Understanding the Equation: Step-by-Step Breakdown", "The equation (2(2w + w) = 48) looks a bit complex at first glance, but it's straightforward once broken down using basic algebraic principles.", "### Step 1: Simplify Inside the Parentheses", "The expression inside the parentheses is (2w + w). Combine the like terms:", "[
\n2w + w = (2 + 1)w = 3w
\n]", "Now substitute back into the equation:", "[
\n2(3w) = 48
\n]", "### Step 2: Multiply Using the Distributive Property", "Next, apply the distributive property. Multiply 2 across (3w):", "[
\n2 \ imes 3w = 6w
\n]", "Now the equation is:", "[
\n6w = 48
\n]", "### Step 3: Solve for (w)", "To isolate (w), divide both sides of the equation by 6:", "[
\nw = \frac{48}{6} = 8
\n]", "---", "## The Solution: (w = 8)", "After carefully simplifying and solving, we find:", "[
\nw = 8
\n]", "This means when (w) equals 8, the original equation (2(2w + w) = 48) is true. You can verify this by substituting (w = 8):", "[
\n2(2(8) + 8) = 2(16 + 8) = 2(24) = 48
\n]", "---", "## Why This Equation Matters: Practical Applications", "While this might appear as a purely academic exercise, equations like (2(2w + w) = 48) model real-life situations, such as:", "- Budgeting or forecasting: If (w) represents a weekly costs or gains, the equation can describe total weekly profit when income and expenses are combined and scaled.
\n- Geometry and measurements: Used in problems involving perimeters, areas, or proportional growth.
\n- Education and teaching: A building block for learning more complex algebra and functions.", "---", "## Mastering Linear Equations: Tips for Success", "1. Simplify first: Always combine like terms inside parentheses before applying multiplication or division.
\n2. Use inverse operations: To isolate variables, use division or subtraction to undo addition or multiplication.
\n3. Check your work: Substitute your solution back into the original equation to confirm correctness.
\n4. Practice regularly: Repetition strengthens fluency in handling different forms of equations.", "---", "## Conclusion", "Solving (2(2w + w) = 48) is a fundamental algebra skill that involves simplifying expressions, applying the distributive property, and isolating the variable. With this step-by-step approach, you now understand not just how to solve it, but why each step matters. Whether for homework help, career preparation, or building confidence in math, mastering this equation opens doors to more advanced problem-solving.", "If you're looking to deepen your fluency, explore additional practice with equations involving distributive property, parentheses, and multi-step word problems. Your journey in algebra continues—and every solved equation is a step forward!", "---", "Keywords: solve (2(2w + w) = 48), algebra equation steps, linear equation solution, how to solve (2(2w + w) = 48), step-by-step algebra, math tutorial, solve for (w), algebra basics, equation solving, step-by-step math, solve linear equations, math practice problems."]
