Substitute: \( 2(3w + w) = 48 \), so \( 8w = 48 \).
["# How to Solve ( 2(3w + w) = 48 ): Step-by-Step Guide to Finding ( w )", "Mathematics often presents equations that look tricky at first glance—but with clear steps, solving them becomes straightforward. In this article, we’ll break down the equation ( 2(3w + w) = 48 ) step by step, showing how to find the value of ( w ), arriving at ( 8w = 48 ), and then solving for ( w ). Whether you’re a student learning algebra or brushing up on fundamentals, this guide will help you understand the process intuitively.", "---", "## Step 1: Simplify Inside the Parentheses", "The equation begins as:", "[\n2(3w + w) = 48\n]", "Inside the parentheses, combine like terms:", "[\n3w + w = 4w\n]", "So the equation becomes:", "[\n2(4w) = 48\n]", "---", "## Step 2: Multiply Inside Parentheses", "Now multiply 2 by ( 4w ):", "[\n2 \ imes 4w = 8w\n]", "Thus, the simplified equation is:", "[\n8w = 48\n]", "---", "## Step 3: Solve for ( w )", "To isolate ( w ), divide both sides of the equation by 8:", "[\nw = \frac{48}{8} = 6\n]", "---", "## Final Answer", "[\nw = 6\n]", "---", "## Why This Matters: The Power of Order of Operations", "Understanding how to simplify expressions like ( 3w + w ) and apply the distributive property is essential in algebra. By following each step carefully, you reinforce key concepts: combining like terms, applying multiplication to terms inside parentheses, and isolating variables. Mastering these steps helps you confidently solve more complex equations and equations with multiple variables.", "---", "### Practice Tip", "Try solving similar equations on your own:", "- ( 4(x + 2) = 32 ) → leads to ( 4x + 8 = 32 ) → ( 4x = 24 ) → ( x = 6 )\n- ( 5(2w - 3) = 35 ) → leads to ( 10w - 15 = 35 ) → ( 10w = 50 ) → ( w = 5 )", "With practice, these patterns become second nature.", "---", "## Summary Keywords (for SEO optimization)\nalgebra equations, solve for ( w ), distribute property, combine like terms, linear equations, math tutorial, intermediate algebra, step-by-step equation solving, 8w = 48, mental math, tips for algebra beginners", "---", "### Learn More\nFor more detailed lessons on algebraic expressions and solving techniques, visit our Algebra Fundamentals section.", "---", "By breaking down ( 2(3w + w) = 48 ) into clear, manageable steps, you’ll master this solution technique and build confidence in tackling algebraic expressions. Practice regularly, and watch your algebra skills grow!"]
