\( \frac{5d + 4d}{400} = 9 \)

["Solving the Equation ( \frac{5d + 4d}{400} = 9 ): A Step-by-Step Guide", "Understanding how to solve linear equations is a fundamental skill in algebra, essential for students, professionals, and lifelong learners. In this article, we’ll explore how to solve the equation:", "[\n\frac{5d + 4d}{400} = 9\n]", "We’ll walk through the process clearly and precisely, helping you master equation solving with confidence.", "---", "### What Equation Are We Solving?", "We begin with the equation:", "[\n\frac{5d + 4d}{400} = 9\n]", "This equation involves simplifying a linear expression in the numerator before dividing, then isolating the variable ( d ).", "---", "### Step 1: Simplify the Numerator", "First, combine like terms in the numerator:", "[\n5d + 4d = 9d\n]", "Now the equation becomes:", "[\n\frac{9d}{400} = 9\n]", "---", "### Step 2: Eliminate the Denominator", "To isolate ( d ), multiply both sides of the equation by 400:", "[\n9d = 9 \ imes 400\n]", "[\n9d = 3600\n]", "---", "### Step 3: Solve for ( d )", "Now divide both sides by 9:", "[\nd = \frac{3600}{9}\n]", "[\nd = 400\n]", "---", "### Final Answer", "[\n\boxed{d = 400}\n]", "---", "### Why Understanding This Equation Matters", "Equations like ( \frac{5d + 4d}{400} = 9 ) appear commonly in real-world applications, such as:", "- Calculating proportions in finance and science\n- Solving for unknowns in physics problems involving rates and distances\n- Building foundations for more complex algebraic concepts", "By mastering how to isolate variables step-by-step, you gain clarity and precision in your mathematical reasoning.", "---", "### Tips for Mastering Linear Equations", "- Always simplify expressions before performing operations.\n- Use inverse operations to isolate the variable.\n- Check your solution by substituting ( d = 400 ) back into the original equation.\n- Practice regularly to build fluency and confidence.", "---", "### Summary", "Solving ( \frac{5d + 4d}{400} = 9 ) yields ( d = 400 ), achieved by combining like terms, multiplying to eliminate denominators, and dividing to isolate the variable. This foundational algebra skill empowers accurate problem-solving across many disciplines.", "---", "Keywords: solve ( \frac{5d + 4d}{400} = 9 ), linear equations, algebra homework help, step-by-step equation solving, math tutorial, basic algebra, equation simplification.\nMeta Description: Learn how to solve the equation ( \frac{5d + 4d}{400} = 9 ) step-by-step. Step through simplifying, isolating, and solving for ( d ), with practical tips and real-world applications."]