Sum: \((n - 1) + n + (n + 1) = 3n = 72\).
["Understanding the Equation: ((n - 1) + n + (n + 1) = 72)", "The algebraic expression ((n - 1) + n + (n + 1) = 72) is a simple yet powerful equation often used to introduce foundational algebra concepts. Let’s explore its step-by-step solution, meaning, and how it illustrates key algebraic principles.", "---", "### Breaking Down the Equation", "The equation:\n[\n(n - 1) + n + (n + 1) = 72\n]", "First, simplify the left-hand side by combining like terms:", "- Combine constants: (-1 + 1 = 0)\n- Combine terms with (n): (n + n + n = 3n)", "So the equation becomes:\n[\n3n = 72\n]", "---", "### Solving for (n)", "To isolate (n), divide both sides by 3:\n[\nn = \frac{72}{3} = 24\n]", "---", "### Why This Equation Matters", "This example demonstrates several fundamental algebraic concepts:", "- Order of Operations: Parentheses first, then addition.\n- Combining Like Terms: Simplifying (n + n + n) and (-1 + 1).\n- Linear Equations: A straightforward equation solved using inverse operations, leading directly to a solution.", "Such equations are essential in teaching basic algebra, reinforcing number sense and problem-solving skills. They also serve as building blocks for more complex mathematical reasoning in topics like equations, functions, and word problems.", "---", "### Step-by-Step Recap", "1. Start with: ((n - 1) + n + (n + 1))\n2. Expand and simplify:\n (-1 + 1 = 0) → (n + n + n = 3n)\n3. Result: (3n = 72)\n4. Solve: (n = 24)", "---", "### Real-World Application", "Equations like this often model real-life scenarios where a sum of adjusted quantities equals a total. For example, balancing payments, total weights, or dividing resources evenly. Understanding how to solve them empowers students and professionals to simplify complex problems into manageable calculations.", "---", "### Summary", "The equation ((n - 1) + n + (n + 1) = 72) elegantly equals (3n = 72), illustrating core algebraic techniques. Solving it reveals (n = 24), but more importantly, it strengthens the ability to manipulate expressions and think logically step by step. Whether in classroom learning or practical computation, mastering such equations is a vital skill in mathematics.", "---", "Keywords: equation simplification, linear equation, algebra basics, solving for (n), step-by-step math, 3n = 72, algebraic practice, solving linear equations, practice problem sum.\nMeta Description: Learn how to solve ((n - 1) + n + (n + 1) = 72) step-by-step, understand simplification and linear equation solving, and grasp its role in foundational algebra."]
