Solve: \( 98 = 2(n-1) \rightarrow n-1 = 49 \rightarrow n = 50 \).
["Solve: ( 98 = 2(n-1) \rightarrow n-1 = 49 \rightarrow n = 50 )", "Solving linear equations is a fundamental skill in algebra, essential for students and professionals alike. In this article, we’ll walk through the step-by-step solution of the equation:\n[\n98 = 2(n - 1)\n]\nto find the value of (n = 50), offering clear insights into algebraic manipulation and problem-solving techniques.", "---", "### Understanding the Equation", "We start with the equation:\n[\n98 = 2(n - 1)\n]\nThis equation states that 98 is equal to two times ((n - 1)). Our goal is to isolate (n) and determine its value.", "---", "### Step 1: Isolate the Parentheses", "To begin solving for (n), divide both sides of the equation by 2 to eliminate the coefficient:\n[\n\frac{98}{2} = \frac{2(n - 1)}{2}\n]\nSimplifying both sides gives:\n[\n49 = n - 1\n]", "---", "### Step 2: Solve for (n)", "Now that we have (49 = n - 1), isolate (n) by adding 1 to both sides:\n[\n49 + 1 = n\n]\n[\nn = 50\n]", "---", "### Final Answer and Summary", "Thus, the solution to the equation (98 = 2(n - 1)) is:\n[\nn = 50\n]", "---", "### Practical Applications and Why It Matters", "This type of equation appears in various real-world scenarios, from calculating total costs (where (n - 1) might represent a group or unit count) to solving geometric problems involving dimensions. Mastering such algebra steps builds confidence and strengthens analytical thinking.", "---", "### Tips for Solving Linear Equations", "- Always isolate the variable term step-by-step.\n- Perform the same operation on both sides to maintain equality.\n- Simplify both sides before solving.\n- Double-check your answer by substituting (n = 50) back into the original equation.", "[\n\ ext{Check:} \quad 2(50 - 1) = 2 \ imes 49 = 98 \quad \ ext{✓}\n]", "---", "### Conclusion", "Solving (98 = 2(n - 1)) step-by-step demonstrates how basic algebraic principles unlock clear solutions. By simplifying and isolating the unknown, anyone can confidently solve such equations, paving the way to more complex mathematical challenges.", "Keywords: solve linear equation, algebra problem, step-by-step solution, (98 = 2(n-1)), how to solve equations, algebraic manipulation, find n, math tutorial, equation solving, educational math."]
