= (10/2)(2×10 + 9d) → 300 = 5(20 + 9d) → 300 = 100 + 45d → 200 = 45d → d = 200/45 ≈ 4.44
["Understanding the Equation: (10/2)(2×10 + 9d) = 300 — Step-by-Step Solution and Easy Calculation", "Breaking down complex algebraic expressions can help demystify mathematical problems and improve problem-solving skills. Today, we’ll walk through a clear, step-by-step solution to the equation:\n(10/2)(2×10 + 9d) = 300, then solve for d, and explain how it leads to d ≈ 4.44.", "---", "### Step 1: Simplify the Left Side of the Equation\nStart with the original equation:\n[\n\left(\frac{10}{2}\right)(2 \ imes 10 + 9d) = 300\n]\nThe fraction simplifies to:\n[\n5(20 + 9d) = 300\n]", "---", "### Step 2: Distribute the Multiplier\nNext, distribute the 5 across the parentheses:\n[\n5 \ imes 20 + 5 \ imes 9d = 300\n]\n[\n100 + 45d = 300\n]", "---", "### Step 3: Isolate the Variable Term\nSubtract 100 from both sides to isolate the term with d:\n[\n45d = 300 - 100\n]\n[\n45d = 200\n]", "---", "### Step 4: Solve for d\nDivide both sides by 45:\n[\nd = \frac{200}{45}\n]\nSimplify the fraction:\n[\nd = \frac{40}{9} \approx 4.44\n]", "---", "### Final Result\n[\n\boxed{d = \frac{200}{45} \approx 4.44}\n]", "---", "### Why This Matters: Real-World Applications\nThis type of algebraic manipulation appears in physics (e.g., calculating uniform acceleration), economics (revenue formulas), and engineering. Understanding how to isolate variables empowers you to solve for unknowns efficiently in any discipline.", "---", "If you’re learning algebra or refining your problem-solving skills, mastering stepwise equation solving is key. Practice with problems similar to this, and soon you’ll handle complex expressions with ease!"]
