-5n + 14.40 = 7.80

["### Understanding the Equation: -5n + 14.40 = 7.80 – A Step-by-Step Guide", "solving linear equations is a fundamental skill in algebra and an essential part of mathematics education. Whether you’re a student learning the basics or someone brushing up on math fundamentals, knowing how to solve equations like -5n + 14.40 = 7.80 helps build confidence in handling algebra. In this article, we’ll explore how to solve this equation step-by-step, explain what each step means, and highlight why mastering these techniques is valuable.", "---", "#### What Is the Equation –5n + 14.40 = 7.80?", "The equation -5n + 14.40 = 7.80 is a linear equation in one variable, where n is unknown. Its goal is to isolate n so we can find the value that makes the equation true. The left-hand side contains a coefficient, variable term, and constant, while the right-hand side is the target value.", "---", "#### Step 1: Simplify if Needed\nIn this case, the equation is straightforward:\n-5n + 14.40 = 7.80\nNo immediate simplification is required between terms.", "---", "#### Step 2: Isolate the Variable Term\nTo isolate the term with n, subtract 14.40 from both sides:", "[\n-5n + 14.40 - 14.40 = 7.80 - 14.40\n]", "Simplifying both sides gives:", "[\n-5n = -6.60\n]", "This step removes the constant from the left side, bringing us closer to solving for n.", "---", "#### Step 3: Solve for n by Dividing by the Coefficient\nThe variable n is multiplied by –5. To isolate n, divide both sides by –5:", "[\nn = \frac{-6.60}{-5}\n]", "Since a negative divided by a negative yields a positive, we get:", "[\nn = \frac{6.60}{5} = 1.32\n]", "---", "#### Final Answer\n[\n\boxed{n = 1.32}\n]", "---", "#### Why This Equation Matters\nUnderstanding how to solve equations like -5n + 14.40 = 7.80 is crucial because:\n- It builds foundational algebra skills.\n- It helps in real-world applications such as budgeting, physics calculations, and data analysis.\n- It improves logical reasoning and problem-solving abilities.", "---", "#### Tips for Solving Linear Equations\n- Always isolate the variable term first by performing inverse operations.\n- Use inverse operations on both sides to maintain equation balance.\n- Double-check your solution by substituting n = 1.32 back into the original equation:", "[\n-5(1.32) + 14.40 = -6.60 + 14.40 = 7.80 \quad \checkmark\n]", "---", "#### Conclusion\nSolving equations step by step empowers you to tackle more complex algebra problems. The equation -5n + 14.40 = 7.80 illustrates the core principles of equation solving — rearranging, simplifying, and isolating variables — in a clear, instructional way. With practice, you’ll find algebraic expressions become intuitive and rewarding.", "---", "Keywords: solve linear equations, algebra basics, equation solving steps, how to solve –5n + 14.40 = 7.80, algebra tutorial for beginners, isolating variables, solving linear equations (n), math practice problems, algebraic expression simplification."]