["Solving the Equation ( 2(2w + w) = 48 ): A Step-by-Step Guide", "Understanding how to solve equations like ( 2(2w + w) = 48 ) is essential for mastering algebra. Whether you're a student tackling homework or someone looking to sharpen problem-solving skills, this equation offers a clear example of simplifying expressions and isolating variables. In this article, we’ll break down the step-by-step process to solve ( 2(2w + w) = 48 ), explain the key algebra concepts involved, and show how this equation relates to real-world scenarios.", "---", "### What Does the Equation ( 2(2w + w) = 48 ) Mean?", "The equation ( 2(2w + w) = 48 ) is a linear equation involving an unknown variable ( w ). The expression inside the parentheses, ( 2w + w ), combines like terms, while the outer coefficient ( 2 ) multiplies the entire sum. Solving this equation means finding the value of ( w ) that makes the equation true.", "---", "### Step 1: Simplify Inside the Parentheses", "Start by simplifying the expression inside the parentheses:", "[
\n2w + w = 3w
\n]", "So the equation becomes:", "[
\n2(3w) = 48
\n]", "---", "### Step 2: Multiply Through", "Now multiply:", "[
\n2 \ imes 3w = 6w
\n]", "Thus, the equation simplifies to:", "[
\n6w = 48
\n]", "---", "### Step 3: Isolate the Variable", "To find ( w ), divide both sides of the equation by 6:", "[
\nw = \frac{48}{6}
\n]", "[
\nw = 8
\n]", "---", "### Step 4: Verify the Solution", "Plug ( w = 8 ) back into the original equation to confirm:", "[
\n2(2(8) + 8) = 2(16 + 8) = 2(24) = 48
\n]", "The left side matches the right side, confirming the solution is correct.", "---", "### Why This Equation Matters: Real-World Applications", "Solving ( 2(2w + w) = 48 ) isn’t just academic—it models real-life problems. For example:", "- Revenue Planning: If ( w ) represents the number of items sold, and total revenue with a 2-fold markup is $48, solving for ( w ) helps determine break-even points.
\n- Distance or Speed: In motion problems, solving for time or rate often uses similar linear forms.
\n- Budgeting: When distributing funds across multiple categories with consistent allocations, such equations help balance budgets accurately.", "---", "### Summary of the Solution", "Given the equation:", "[
\n2(2w + w) = 48
\n]", "- Simplify to ( 6w = 48 )
\n- Solve: ( w = 8 )
\n- Verified: This value satisfies the original equation.", "---", "### Tips for Solving Similar Equations", "- Always simplify expressions inside parentheses first.
\n- Multiply coefficients carefully.
\n- When isolating ( w ), use inverse operations: divide, subtract, add.
\n- Always check your solution by substituting it back into the original equation.", "---", "Mastering equations like ( 2(2w + w) = 48 ) builds the foundation for more complex algebra and critical thinking. With practice, you’ll approach similar problems with confidence, turning abstract symbols into powerful tools for problem-solving.", "Keywords: solve linear equation, algebra tips, how to solve 2(2w + w) = 48, step-by-step algebra, equation solving, real-world math,w equation solution, mathematical problem solving", "Meta Description: Learn step-by-step how to solve ( 2(2w + w) = 48 ) with clear explanations, verification, and real-life applications. Perfect for students and algebra learners."]
