Simplify: \( 2(4w) = 96 \) → \( 8w = 96 \)
["# How to Simplify ( 2(4w) = 96 ) Step by Step: A Clear Guide", "Solving equations like ( 2(4w) = 96 ) might seem intimidating at first, but breaking it down step by step makes it easy to understand and solve. This article walks you through simplifying the expression ( 2(4w) = 96 ) to solve for ( w ), explaining each step clearly—perfect for students, math enthusiasts, or anyone looking to improve their algebraic skills.", "---", "## Understanding the Equation: ( 2(4w) = 96 )", "The equation ( 2(4w) = 96 ) starts with parentheses and multiplication on the left side. To simplify and solve for ( w ), we need to follow fundamental algebraic rules step by step.", "---", "## Step 1: Simplify Inside the Parentheses", "Inside the parentheses, we see ( 2 \ imes 4w ). Multiplying constants first:", "[\n2(4w) = 8w\n]", "So,\n[\n2(4w) = 96 \quad \ ext{becomes} \quad 8w = 96\n]", "---", "## Step 2: Isolate the Variable ( w )", "Now the equation is ( 8w = 96 ). To solve for ( w ), divide both sides by 8 (the coefficient of ( w )):", "[\nw = \frac{96}{8}\n]", "[\nw = 12\n]", "---", "## Why This Works: The Order of Operations", "Simplifying ( 2(4w) ) begins with the multiplication property of left-hand side, combining coefficients before dealing with the variable. Then, by dividing both sides by 8, we apply the principle that equality must be maintained—performing the same operation on both sides.", "---", "## Final Answer", "So, the simplified form of ( 2(4w) = 96 ) leads directly to:", "[\n\boxed{w = 12}\n]", "---", "## Additional Tips for Solving Similar Equations", "- Always simplify expressions inside parentheses first.\n- Perform multiplications before dividing.\n- Apply inverse operations to isolate the variable.\n- Check your solution by substituting back into the original equation.", "---", "## Verification: Double-Checking Your Work", "Plug ( w = 12 ) into the original equation:", "[\n2(4 \ imes 12) = 2(48) = 96\n]", "The left side equals the right side, confirming the solution is correct.", "---", "## Conclusion", "Simplifying ( 2(4w) = 96 ) to ( w = 12 ) relies on basic algebra: combining coefficients, using inverse multiplication, and maintaining equation balance. Mastering these steps builds confidence in solving more complex equations.", "Keywords: simplify equation, algebra tips, solve for w, step-by-step math, linear equation, math fundamentals, equation solving guide, how to simplify 2(4w) = 96", "Meta description: Learn how to simplify ( 2(4w) = 96 ) into ( w = 12 ) with step-by-step explanation. Perfect for students mastering algebra basics."]
