\frac{5d + 4d}{400} = 9 \quad \Rightarrow \quad \frac{9d}{400} = 9

["# Solve the Equation: ( \frac{5d + 4d}{400} = 9 \Rightarrow \frac{9d}{400} = 9 )", "If you're learning algebra, you probably encounter equations like this frequently:\n[\n\frac{5d + 4d}{400} = 9\n]\nBut what does this really mean? How do we solve it step-by-step? In this article, we break down the equation, simplify it clearly, and solve for ( d ), giving you a solid understanding of linear equation solving.", "---", "## Step-by-Step Breakdown of the Equation", "We start with:\n[\n\frac{5d + 4d}{400} = 9\n]", "### Step 1: Simplify the Numerator", "Add the like terms in the numerator — (5d + 4d):\n[\n5d + 4d = 9d\n]\nSo the equation becomes:\n[\n\frac{9d}{400} = 9\n]", "### Step 2: Eliminate the Denominator", "Multiply both sides of the equation by 400 to eliminate the denominator:\n[\n400 \cdot \frac{9d}{400} = 9 \cdot 400\n]\n[\n9d = 3600\n]", "### Step 3: Solve for ( d )", "Now divide both sides by 9:\n[\nd = \frac{3600}{9} = 400\n]", "---", "## Final Answer", "[\n\boxed{d = 400}\n]", "---", "## Why Understanding This Equation Matters", "This simple algebra problem demonstrates key algebra fundamentals: combining like terms, manipulating equations, and isolating variables. Mastering these steps builds your foundation for solving more complex problems in science, engineering, economics, and beyond.", "---", "## Pro Tips for Solving Linear Equations Like This", "- Always simplify expressions in the numerator or denominator first.\n- Use inverse operations (multiplication/division) to eliminate denominators.\n- Isolate your variable term by performing the same operation on both sides.\n- Double-check your solution by substituting back into the original equation.", "---", "### Want More?\nCheck out our guides on solving multi-step equations, working with variables in denominators, and applying algebra in real-life problems!", "---", "Keywords: algebra equation, solve (\frac{5d + 4d}{400} = 9), step-by-step solution, linear equations, divide by 400, isolate (d), mathematical reasoning, solving (\frac{9d}{400} = 9), algebra practice.", "---", "Summary: Simplify (5d + 4d) to (9d), then solve (\frac{9d}{400} = 9) by multiplying both sides by 400 and dividing by 9 to get (d = 400). You’ve solved the equation correctly and clearly!"]