["Simplify: 2(4w) = 64 → 8w = 64 – A Step-by-Step Explanation", "Whether you're a student learning algebra or just looking to sharpen your equation-solving skills, simplifying expressions like ( 2(4w) = 64 ) is a fundamental step. In this article, we’ll walk through how to simplify the equation step by step to find the value of ( w ), while also explaining the underlying principles.", "---", "### Step 1: Understand the Original Equation", "We start with:
\n[ 2(4w) = 64 ]", "This equation says that twice four times ( w ) equals 64. Our goal is to isolate ( w ) on one side to solve for it.", "---", "### Step 2: Simplify the Left Side", "Multiply ( 2 \ imes 4w ):
\n[ 2(4w) = 8w ]", "So the equation becomes:
\n[ 8w = 64 ]", "This simplification reduces the expression clearly and sets the stage for solving for ( w ).", "---", "### Step 3: Solve for ( w )", "To isolate ( w ), divide both sides of the equation by 8:
\n[ w = \frac{64}{8} ]
\n[ w = 8 ]", "---", "### Why This Simplification Matters", "Simplifying expressions algebraically is essential in math and science because it:
\n- Makes equations easier to analyze and solve
\n- Reduces errors by minimizing complexity
\n- Builds a strong foundation for tackling advanced algebra and calculus", "---", "### Final Answer
\n[ w = 8 ]", "---", "Key Takeaways:
\n- Use the distributive property to simplify expressions like ( 2(4w) )
\n- Keep equivalent forms consistent when simplifying
\n- Isolate the variable by applying inverse operations on both sides", "Mastering these basic simplification steps empowers you to solve more complex equations with confidence. Start simplifying today and watch your algebra skills grow!"]
