Substitute the length: 2(3w + w) = 64 → 8w = 64 → \( w = 8 \) meters.
["Substitute and Solve: How to Solve 2(3w + w) = 64 for w in Simple Algebraic Steps", "Understanding algebra often involves simplifying expressions and isolating variables. One common problem in algebra is solving linear equations by substituting and simplifying both sides efficiently. Let’s explore a classic example: replacing the expression ( 2(3w + w) = 64 ) to find that ( w = 8 ) meters. This clear walkthrough helps students master substitution and solving techniques with confidence.", "---", "### The Equation in Focus:\n2(3w + w) = 64", "---", "### Step 1: Simplify Inside the Parentheses\nStart by simplifying the expression inside the parentheses:\n( 3w + w = 4w )\nSo the equation becomes:\n2(4w) = 64", "---", "### Step 2: Apply the Distributive Property\nMultiply the 2 into the term ( 4w ):\n( 2 × 4w = 8w ), giving:\n8w = 64", "---", "### Step 3: Isolate the Variable\nTo solve for ( w ), divide both sides by 8:\n( w = \frac{64}{8} = 8 )", "---", "### Final Step: Present the Result\nThus, the solution is:\nw = 8 meters", "---", "### Why This Process Matters\nThis example demonstrates how substitution and simplification eliminate complexity step-by-step:\n- Combining like terms reduces the expression.\n- Multiplication distributes evenly.\n- Division isolates the variable.", "Whether you’re a student learning algebra or a educator teaching key problem-solving steps, understanding substitution and simplification lays a solid foundation for tackling more complex equations.", "---", "### Summary\nSolve ( 2(3w + w) = 64 ) by:\n1. Simplifying inside parentheses: ( 3w + w = 4w )\n2. Multiplying by 2: ( 2 × 4w = 8w )\n3. Dividing to isolate ( w ): ( w = 8 )", "Final Answer: w = 8 meters", "---", "For further practice, solve similar equations using substitution techniques and remember: breaking down expressions carefully leads to clear solutions!"]
