\( 145 = 50 + 45d \)

["Understanding the Equation: 145 = 50 + 45d", "The equation ( 145 = 50 + 45d ) is a foundational algebraic expression widely used in solving for unknown variables. This type of linear equation appears in various practical scenarios, from basic math problems to real-world applications in science, engineering, and finance. In this SEO-optimized article, we break down the equation, solve it step-by-step, and explore its relevance in everyday contexts.", "---", "### What Does ( 145 = 50 + 45d ) Mean?", "The equation ( 145 = 50 + 45d ) states that when 50 is added to 45 times an unknown value ( d ), the result is 145. This structure is common in algebra, where one side represents a constant value, and the other side includes a constant plus a term multiplied by a variable. Solving this equation helps isolate ( d ), revealing its numerical value.", "---", "### Step-by-Step Solution", "To solve for ( d ), follow these simple algebraic steps:", "1. Start with the original equation:\n [\n 145 = 50 + 45d\n ]", "2. Subtract 50 from both sides to eliminate the constant on the right:\n [\n 145 - 50 = 45d\n ]\n [\n 95 = 45d\n ]", "3. Divide both sides by 45 to isolate ( d ):\n [\n d = \frac{95}{45}\n ]", "4. Simplify the fraction:\n [\n d = \frac{19}{9} \approx 2.11\n ]", "So, the solution is ( d = \frac{19}{9} ), approximately 2.11.", "---", "### Why Is This Equation Useful?", "Linear equations like ( 145 = 50 + 45d ) help model relationships where one quantity depends linearly on another. Here are some practical applications:", "- Budgeting and Finance: Calculating the number of units needed to reach a financial goal, factoring in fixed and variable costs.\n- Science and Engineering: Measuring rates of change, such as speed, growth, or chemical reaction rates.\n- Everyday Problem Solving: Determining time, distance, or cost when partial information is known.", "---", "### Alternative Forms and Interpretations", "You can rewrite the equation in different ways to suit different needs:", "- Slope-Intercept Form: Solving for ( d ) gives ( d = \frac{1}{45}(145 - 50) ), showing slope and intercept clearly.\n- Verbal Explanation: “145 equals fifty plus forty-five times d” clarifies the real-world scenario behind the numbers.", "---", "### Common Questions and FAQs", "Q: How do I check if my solution is correct?\nA: Substitute ( d = \frac{19}{9} ) back into the original equation:\n[ 50 + 45 \left( \frac{19}{9} \right) = 50 + 95 = 145 ]\n✓ Verified!", "Q: Can this equation model real-life situations?\nA: Yes, for example, if a delivery fee is $50 and $45 is charged per mile, the equation calculates miles driven to reach a total fare of $145.", "---", "### Conclusion", "The equation ( 145 = 50 + 45d ) is a clear and useful example of linear algebra in action. Mastering such equations sharpens problem-solving skills and supports logical thinking in mathematics and beyond. Whether you’re a student learning algebra or a professional using math to analyze data, understanding how to isolate variables and interpret equations is essential.", "---", "Related Keywords for SEO:\n algebra equation solve linear equations, how to solve 145 = 50 + 45d, step-by-step algebra solution, linear equation everywhere, real-world algebra examples, equation solving tutorial", "---", "Optimized for search engines with clear structure, explanatory content, and keyword relevance, this article helps readers find, understand, and apply the math behind ( 145 = 50 + 45d ) with confidence."]