Equate and solve: \(5000 + 20x = 50x\).
["Solving the Equation (5000 + 20x = 50x): A Step-by-Step Guide", "When faced with the equation (5000 + 20x = 50x), solving for (x) becomes an intuitive process using basic algebraic principles. This article guides you through solving linear equations like this one with clear explanations, making it easy to understand and apply in similar real-world scenarios—such as budgeting, finance, or proportional reasoning.", "---", "### Step 1: Understand the Equation", "The equation is:", "[\n5000 + 20x = 50x\n]", "Here, (x) is an unknown variable—commonly representing a quantity such as hours worked, units produced, or乘数 (multiplier). The goal is to isolate (x) and determine its exact value.", "---", "### Step 2: Move All Terms Involving (x) to One Side", "Start by eliminating the variable term from one side to simplify. Subtract (20x) from both sides:", "[\n5000 + 20x - 20x = 50x - 20x\n]", "This simplifies to:", "[\n5000 = 30x\n]", "Now only one (x)-term remains, facilitating a straightforward division.", "---", "### Step 3: Solve for (x) by Isolating It", "To solve for (x), divide both sides by 30:", "[\nx = \frac{5000}{30}\n]", "Simplify the fraction:", "[\nx = \frac{500}{3} \approx 166.67\n]", "Thus, the solution is:", "[\nx = \frac{500}{3}\n]", "---", "### Step 4: Verify the Solution", "Plug (x = \frac{500}{3}) back into the original equation to confirm correctness:", "- Left side:\n (5000 + 20\left(\frac{500}{3}\right) = 5000 + \frac{10000}{3} = \frac{15000 + 10000}{3} = \frac{25000}{3})", "- Right side:\n (50 \ imes \frac{500}{3} = \frac{25000}{3})", "Both sides are equal, confirming the solution is correct.", "---", "### Why This Equation Matters", "Such linear equations model practical problems—like balancing costs, profits, or rates. For example:", "- If a company pays a fixed cost of $5,000 monthly and a variable cost of $20 per unit produced ((20x)), and generates $50 per unit ((50x)), solving (5000 + 20x = 50x) determines the break-even point where total receipts equal total costs.", "---", "### Final Answer", "[\n\boxed{x = \frac{500}{3}}\n]", "Understanding how to solve equations like (5000 + 20x = 50x) equips learners with essential algebra skills applicable across science, business, and daily decision-making.", "---", "Keywords:\nsolve linear equation, algebra tutorial, fix x in equation, step-by-step solution, math problem solving, equation simplification, real-world math applications", "Related Topics:\nhow to solve 20x equations, breaking even calculation, algebraic word problems, solving linear equations, step-by-step algebra solve"]
