3n + 14.40 - 8n = 7.80

["Understanding the Algebraic Equation: 3n + 14.40 – 8n = 7.80 – Exploring Solutions & Applications", "When tackling algebraic equations, simplifying expressions and solving for variables are essential skills in mathematics. One such equation that frequently appears in middle and high school curricula is:", "3n + 14.40 – 8n = 7.80", "At first glance, this linear equation may seem straightforward, but mastering its solution helps strengthen algebraic reasoning. In this article, we’ll break down the equation step by step, solve for ( n ), and explore its real-world applications and learning value.", "---", "### Solving the Equation Step-by-Step", "Let’s start with the original equation:", "[\n3n + 14.40 - 8n = 7.80\n]", "#### Step 1: Combine like terms on the left-hand side", "Combine the ( n )-terms:", "[\n(3n - 8n) + 14.40 = 7.80\n]\n[\n-5n + 14.40 = 7.80\n]", "#### Step 2: Isolate the term with ( n )", "Subtract 14.40 from both sides:", "[\n-5n = 7.80 - 14.40\n]\n[\n-5n = -6.60\n]", "#### Step 3: Solve for ( n )", "Divide both sides by -5:", "[\nn = \frac{-6.60}{-5} = 1.32\n]", "---", "### Verification: Check the Solution", "Plugging ( n = 1.32 ) back into the original equation:", "[\n3(1.32) + 14.40 - 8(1.32) = 3.96 + 14.40 - 10.56 = 7.80\n]", "The equation holds true, confirming our solution.", "---", "### Why This Equation Matters: Applications & Learning Benefits", "Solving equations like 3n + 14.40 – 8n = 7.80 offers more than just a numerical answer—it builds critical thinking and analytical skills used across science, engineering, and finance.", "Real-World Applications:\n- Finance: Calculating break-even points where costs and revenues balance.\n- Physics: Determining unknown variables in motion equations, such as time or distance.\n- Engineering: Designing systems where input and output must match precisely.", "Learning Benefits:\n- Strengthens algebraic manipulation and equation solving.\n- Enhances logical reasoning by breaking complex expressions into manageable steps.\n- Prepares students for advanced math topics like linear systems and functions.", "---", "### Key Takeaways", "- The solution to ( 3n + 14.40 - 8n = 7.80 ) is ( n = 1.32 ).\n- Simplifying like terms and isolating variables are key steps.\n- Verifying solutions ensures accuracy and reinforces problem-solving rigor.\n- Understanding these equations prepares learners for more advanced STEM applications.", "---", "### Practice Tips", "If you’re tackling similar problems, remember:\n- Always combine like terms carefully.\n- Keep signs consistent when subtracting or adding.\n- Verify solutions by substitution.\n- Relate algebraic expressions to real-life situations to deepen understanding.", "---", "By mastering equations like 3n + 14.40 – 8n = 7.80, students build a solid foundation for mathematical fluency and problem-solving success in academics and beyond. Keep practicing—operations with linear expressions are your stepping stones to mastery!", "---", "Key Terms for SEO:\nalgebraic equation, solve for n, 3n + 14.40 - 8n = 7.80, linear equation, math problem solving, high school algebra, real-world applications of equations, equation solving tutorial."]