2x + x + (x - 10,000) = 120,000 \Rightarrow 4x = 130,000 \Rightarrow x = 32,500

["# Solving the Equation 2x + x + (x - 10,000) = 120,000: Step-by-Step Explanation", "Mathematics often presents challenges when equations require careful step-by-step breakdown — especially when combining variables and constants. One such problem is the linear equation:", "2x + x + (x - 10,000) = 120,000", "At first glance, this equation may seem straightforward, but understanding each step ensures accuracy and builds stronger problem-solving skills. In this article, we’ll walk through solving this equation step-by-step, arriving at the solution x = 32,500, and explain how this relates to real-world applications and algebraic principles.", "---", "## Step 1: Combine Like Terms on the Left Side", "The left side of the equation contains three terms involving x:\n- 2x\n- x\n- (x - 10,000)", "We simplify by combining all terms with x:", "[ 2x + x + x - 10,000 ]", "Combine coefficients:", "[ (2 + 1 + 1)x - 10,000 = 4x - 10,000 ]", "So the equation simplifies to:", "4x - 10,000 = 120,000", "---", "## Step 2: Isolate the Variable Term", "To solve for x, start by eliminating the constant on the left side. Add 10,000 to both sides:", "[\n4x - 10,000 + 10,000 = 120,000 + 10,000\n]", "[\n4x = 130,000\n]", "This step isolates the variable portion and prepares for division.", "---", "## Step 3: Solve for x", "Now divide both sides by 4 to isolate x:", "[\nx = \frac{130,000}{4} = 32,500\n]", "---", "## Why This Equation Matters", "This equation models linear relationships frequently used in finance, budgeting, and data analysis. For example, combining costs or income sources often results in expressions like 2x + x + (x - fixed cost), simplified to 4x - constant = total amount.", "Solving such equations provides precise values — in this case, showing that an unknown quantity (x), representing a base amount, equals 32,500 when scaled by real-world constraints (such as a fixed shortage of 10,000 in a budget).", "---", "## Final Thoughts", "Understanding each step — combining like terms, isolating variables, and simplifying — builds confidence in handling algebra. The equation 2x + x + (x - 10,000) = 120,000 is a classic example of linear algebra with practical meaning. By applying these rules methodically, you can solve similar problems accurately and efficiently.", "Whether you’re a student, teacher, or professional, mastering such equations enhances analytical thinking and problem-solving discipline.", "---", "Key takeaways:", "- Combine like terms to simplify expressions.\n- Isolate the variable term by eliminating constants.\n- Use basic arithmetic and division to solve for the unknown.\n- Real-world problems often boil down to linear equations like this.", "If you’re struggling with similar equations, practice step-by-step simplification — power comes from precision!", "---", "Want more tips on solving algebra problems? Check out our guides on linear equations, variable elimination, and real-world math applications!"]