Simplify and solve for \( w \): \( 2(4w) = 64 \), \( 8w = 64 \), \( w = 8 \).

["How to Simplify and Solve the Equation ( 2(4w) = 64 ) – A Step-by-Step Guide", "Solving linear equations is a fundamental skill in algebra, and understanding how to simplify and solve for ( w ) can make math much easier. In this article, we’ll break down the process of solving the equation ( 2(4w) = 64 ) step-by-step, showing exactly how we arrive at ( w = 8 ).", "---", "### Step 1: Understand the Equation\nWe begin with the equation:\n[\n2(4w) = 64\n]\nThis means "2 times 4 times ( w )" equals 64. Our goal is to isolate ( w ) and find its value.", "---", "### Step 2: Simplify the Left Side\nStart by simplifying the expression on the left:\n[\n2(4w) = 8w\n]\nSo the equation now becomes:\n[\n8w = 64\n]\nThis simplification reduces the complexity, making it easier to solve for ( w ).", "---", "### Step 3: Solve for ( w )\nTo isolate ( w ), divide both sides of the equation by 8:\n[\nw = \frac{64}{8}\n]\n[\nw = 8\n]", "---", "### Step 4: Verify the Solution\nIt’s always good practice to check your answer by substituting ( w = 8 ) back into the original equation:\n[\n2(4 \ imes 8) = 2(32) = 64\n]\nSince the left side equals the right side, our solution is correct.", "---", "### Final Answer\nSimplifying and solving ( 2(4w) = 64 ) leads directly to:\n[\nw = \boxed{8}\n]", "---", "### Why Simplifying Matters\nBreaking down expressions step-by-step helps avoid mistakes and clears up confusion. Simplifying ( 2(4w) ) into ( 8w ) makes the next step—dividing by 8—clear and logical. Mastering this process strengthens your algebra foundation and prepares you for more complex equations.", "---", "Start with simplifying, then isolate the variable—this proven method makes solving for ( w ) quick and reliable!"]