Simplify: \( 8w = 64 \) implies \( w = 8 \).
["How to Simplify ( 8w = 64 ) to Find ( w = 8 ) – A Step-by-Step Guide", "Learning to simplify equations is a fundamental skill in algebra and mathematics. One of the most straightforward examples is solving the equation ( 8w = 64 ) to find the value of ( w ). This article explains how to solve this simple linear equation clearly, step by step, and why the solution is ( w = 8 ). Understanding this process helps build a strong foundation for more complex algebraic concepts.", "### Understanding the Equation ( 8w = 64 )", "In algebra, solving an equation means finding the value of the unknown variable—here, ( w )—that makes the equation true. The equation ( 8w = 64 ) states that eight times an unknown number ( w ) equals 64. To determine what ( w ) is, we need to isolate ( w ) on one side of the equation.", "### Step 1: Divide Both Sides by 8", "To isolate ( w ), divide both sides of the equation by 8:", "[\n\frac{8w}{8} = \frac{64}{8}\n]", "Simplifying both sides:", "- Left side: ( \frac{8w}{8} = w )\n- Right side: ( \frac{64}{8} = 8 )", "So, the equation becomes:", "[\nw = 8\n]", "### Why This Works: The Science of Balance", "Algebra maintains a balance—whatever operation you apply to one side must be applied to the other. Dividing both sides by 8 preserves equality, leaving only ( w ) alone on the left. This step straightforwardly removes the coefficient of 8 attached to ( w ).", "### Verifying the Solution", "It’s always good practice to verify your answer by substituting back into the original equation:", "[\n8w = 64\n]\n[\n8(8) = 64\n]\n[\n64 = 64 \quad \ ext{(True)}\n]", "This confirms that ( w = 8 ) is indeed the correct solution.", "### Real-W-world Applications", "This kind of simple equation is everywhere—whether calculating unit prices, scaling recipes, or planning budgets. Knowing how to solve for a variable helps you make clear, accurate decisions with real-life numbers.", "---", "Summary:\n- Equation: ( 8w = 64 )\n- Solve by dividing both sides by 8 → ( w = 8 )\n- Verification confirms correctness\n- Essential skill for algebra and daily math", "Simplifying ( 8w = 64 ) to ( w = 8 ) is a clear example of variable isolation, the cornerstone of algebraic problem-solving. Master this step, and you’ll be well-prepared for more advanced equations.", "---", "Keywords: solve linear equation, simplify ( 8w = 64 ), algebraic isolation, step-by-step math, equation solving tips, divide both sides algebra, verify solution, find ( w ), beginner algebra."]
