\(0.06x + 2,000 - 0.04x = 2,600\) → \(0.02x = 600\) → \(x = 30,000\).

["# Solving Linear Equations: Step-by-Step Guide to (0.06x + 2,000 - 0.04x = 2,600)", "Solving linear equations is a fundamental skill in algebra that appears frequently in math education and real-world problem solving. Today, we’ll walk through the step-by-step solution of a classic linear equation:", "[\n0.06x + 2,000 - 0.04x = 2,600\n]\nwhich simplifies to (0.02x = 600), and finally, (x = 30,000).", "---", "## Understanding the Equation", "Begin with the original equation:\n[\n0.06x + 2,000 - 0.04x = 2,600\n]", "This equation combines variable terms ((0.06x) and (-0.04x)) with constant terms (2,000), equated to a constant on the right-hand side. The goal is to isolate (x) and solve for it.", "---", "## Step 1: Combine Like Terms", "Group the (x)-terms on the left side:\n[\n(0.06x - 0.04x) + 2,000 = 2,600\n]", "Simplify the coefficients:\n[\n0.02x + 2,000 = 2,600\n]", "---", "## Step 2: Isolate the Variable Term", "Subtract 2,000 from both sides to move the constant to the right:\n[\n0.02x = 2,600 - 2,000\n]\n[\n0.02x = 600\n]", "---", "## Step 3: Solve for (x)", "Divide both sides by 0.02 to isolate (x):\n[\nx = \frac{600}{0.02}\n]", "Divide 600 by 0.02:\n[\nx = 600 \div 0.02 = 30,000\n]", "---", "## Why This Matters", "Solving linear equations like this is essential in fields ranging from finance and economics to engineering and computer science. This particular problem demonstrates how to simplify expressions, combine like terms, and isolate variables — key skills for more advanced algebra and beyond.", "---", "## Final Answer", "[\n\boxed{x = 30,000}\n]", "---", "## Further Practice Tips", "- Try similar equations with different coefficients.\n- Practice translating word problems into algebraic expressions.\n- Use graphing tools to visualize how linear equations behave.", "By mastering these techniques, you’ll build a strong foundation for tackling complex equations and developing analytical thinking."]