Substitute: \(2((2w + 3) + w) = 54\).
["# Solving the Equation: Understanding the Substitute (2((2w + 3) + w) = 54)", "In algebra, solving equations step by step is essential for finding unknown values reliably. One common problem students encounter involves substitute expressions and simplify them before solving. Today, we focus on a clean, step-by-step breakdown of the equation:", "[\n2((2w + 3) + w) = 54\n]", "This equation uses substitution through nested expressions — an important skill for algebra and beyond. Let’s solve it efficiently and understand each step.", "---", "## Step 1: Simplify the Expression Inside the Brackets", "The left side contains a nested expression:\n[\n(2w + 3) + w\n]", "Combine like terms:", "[\n2w + w + 3 = 3w + 3\n]", "Now substitute this back:", "[\n2((3w + 3)) = 54\n]", "---", "## Step 2: Simplify the Entire Left Side", "Multiply inside the outer parentheses:", "[\n2(3w + 3) = 6w + 6\n]", "Your equation becomes:", "[\n6w + 6 = 54\n]", "---", "## Step 3: Solve for (w)", "Subtract 6 from both sides:", "[\n6w = 48\n]", "Now divide both sides by 6:", "[\nw = 8\n]", "---", "## Final Answer", "The value that solves the equation is:", "[\n\boxed{w = 8}\n]", "---", "## Why This Matters: The Role of Substitution in Algebra", "The expression (2((2w + 3) + w)) demonstrates substitution — replacing expressions with variables to simplify complex equations before solving. Mastering this method helps tackle advanced algebra, functions, and real-world modeling faster and more accurately.", "---", "## Tips to Solve Similar Problems Easily", "- Simplify inner parentheses first before expanding or combining terms.\n- Write each step clearly to avoid mistakes.\n- Always isolate the variable on one side before dividing.\n- Check your solution by plugging (w = 8) back into the original equation.", "Verify:", "[\n2((2 \ imes 8 + 3) + 8) = 2((16 + 3) + 8) = 2(19 + 8) = 2 \ imes 27 = 54\n]", "Correct!", "---", "# Keywords for SEO Optimization:\n- Solve (2((2w + 3) + w) = 54)\n- Step-by-step algebra equation solving\n- Simplify nested expressions algebra\n- How to solve linear equations with substitution\n- Algebraic substitution techniques\n- Learn algebra with practice problems", "Start mastering your algebra today — substitution made easy!"]
