\(2(3w + w) = 64\),
["# Solving (2(3w + w) = 64): A Step-by-Step Guide and Full Explanation", "Understanding how to solve equations like (2(3w + w) = 64) is essential for mastering algebra. Whether you're a student learning basic problem-solving or a parent helping with homework, knowing how to simplify and solve linear equations is key. This article breaks down the step-by-step solution to (2(3w + w) = 64) and explains each part clearly — including why these steps work.", "---", "## What Equation Are We Solving?", "We are given:", "[\n2(3w + w) = 64\n]", "This is a linear equation in one variable ((w)). Our goal is to isolate (w) and find its value.", "---", "## Step 1: Simplify Inside the Parentheses", "Start by simplifying the expression inside the parentheses: (3w + w).", "Since both terms involve (w), combine like terms:", "[\n3w + w = 4w\n]", "Now the equation becomes:", "[\n2(4w) = 64\n]", "---", "## Step 2: Multiply Inside", "Next, multiply (2) by (4w):", "[\n2 \ imes 4w = 8w\n]", "So now the equation is simplified to:", "[\n8w = 64\n]", "---", "## Step 3: Solve for (w)", "To isolate (w), divide both sides of the equation by 8:", "[\nw = \frac{64}{8} = 8\n]", "---", "## Final Answer", "[\n\boxed{w = 8}\n]", "---", "## How to Verify: Plug Back into Original Equation", "Always verify your solution by substituting (w = 8) into the original equation:", "[\n2(3(8) + 8) = 2(24 + 8) = 2(32) = 64\n]", "The left side equals the right side, confirming that our solution is correct.", "---", "## Why This Equation Matters", "Solving equations like (2(3w + w) = 64) builds foundational algebra skills. These types of linear equations appear frequently in math, science, economics, and everyday problem-solving — such as calculating costs, determining rates, or predicting results.", "---", "## Summary of Steps", "1. Combine like terms inside parentheses: (3w + w = 4w).\n2. Multiply: (2 \ imes 4w = 8w).\n3. Isolate (w): (8w = 64), then divide: (w = 8).\n4. Verify: Check by substituting back.", "---", "Mastering these steps ensures you can approach similar equations confidently. Practice makes perfect — next time try (3(2x - 4) = 18) or other variations to strengthen your skills!", "---", "Keywords: equation solving, linear equation, algebra tutorial, solve (2(3w + w) = 64), step-by-step, math homework help, verify solution, simplify expressions, algebraic methods."]
