Solving, \( 2 \times 4w = 64 \) leads to \( 8w = 64 \), so \( w = 8 \).
["Solving ( 2 \ imes 4w = 64 ): Step-by-Step Guide to Find ( w = 8 )", "Mathematics often involves simplifying expressions to solve for unknown variables. One classic example is solving the equation ( 2 \ imes 4w = 64 ). Understanding how to simplify this equation not only helps in finding the correct value but also strengthens foundational algebra skills. In this article, we’ll walk through solving ( 2 \ imes 4w = 64 ) step-by-step, revealing how the solution leads to ( w = 8 ).", "---", "### The Given Equation: ( 2 \ imes 4w = 64 )", "We start with the expression on the left-hand side: ( 2 \ imes 4w ). Multiplication is associative and commutative, so we can multiply the constants:", "[\n2 \ imes 4w = (2 \ imes 4) \ imes w = 8w\n]", "Rewriting the equation:", "[\n8w = 64\n]", "This simplified form makes solving for ( w ) straightforward.", "---", "### Isolating the Variable ( w )", "To find ( w ), divide both sides of the equation by 8:", "[\nw = \frac{64}{8}\n]", "Simplify the fraction:", "[\nw = 8\n]", "---", "### Understanding the Steps", "- Step 1: Combine like terms in multiplication: ( 2 \ imes 4w = 8w ).\n- Step 2: Replace the expression: ( 8w = 64 ).\n- Step 3: Divide both sides by 8 to isolate ( w ): ( w = \frac{64}{8} = 8 ).", "This clear, linear path ensures accuracy and demonstrates a key algebraic principle — simplifying expressions before solving.", "---", "### Why This Method Works", "Linear equations like ( 8w = 64 ) are solved by inverse operations. Since ( 8w ) means ( 8 \ imes w ), dividing both sides by 8 reverses the multiplication, leaving ( w ) alone. This method is reliable and forms the basis of solving more complex equations in algebra.", "---", "### Final Answer", "[\n\boxed{w = 8}\n]", "---", "### Conclusion", "Solving ( 2 \ imes 4w = 64 ) to ( 8w = 64 ), then dividing by 8 confirms that ( w = 8 ). By breaking each step clearly, we see how algebra transforms equations into solutions — a valuable skill applicable across mathematics and real-world problem solving.", "---", "Keywords: solve ( 2 \ imes 4w = 64 ), algebra steps, solve for ( w ), step-by-step equation solving, how to find ( w ), understanding linear equations, intermediate algebra, simplifying expressions, divide both sides, basic algebra."]
