Solving: 150 = 0.20(500 + x)

["Solving the Equation: 150 = 0.20(500 + x) | Step-by-Step Guide", "When faced with an equation like 150 = 0.20(500 + x), many students feel overwhelmed—or unsure where to begin. But with a clear, step-by-step approach, solving this equation becomes straightforward and even satisfying. Whether you're a student learning algebra or someone brushing up on essential math skills, this guide will walk you through solving 150 = 0.20(500 + x) efficiently and confidently.", "---", "### What Does This Equation Mean?", "The equation expresses a real-world relationship: something equals 20% (or 0.20) of a total that includes a fixed value (500) plus an unknown variable (x). This kind of problem shows up in budgeting, pricing, interest calculations, and everyday decision-making.", "---", "### Step 1: Understand the Structure", "Begin by recognizing the form:\nA = r × (C + x)\nwhere:\n- A = 150 (known total)\n- r = 0.20 (the rate, 20% as a decimal)\n- C = 500 (fixed cost or base amount)\n- x = ? (the unknown variable)", "So, 150 equals 20% of (500 plus x). The goal is to isolate x.", "---", "### Step 2: Isolate the Parent Expression", "Start by dividing both sides of the equation by 0.20 to eliminate the coefficient:", "[\n\frac{150}{0.20} = 500 + x\n]", "Calculate the left side:", "[\n\frac{150}{0.20} = 150 \div 0.2 = 750\n]", "Now the equation becomes:", "[\n750 = 500 + x\n]", "---", "### Step 3: Solve for x", "Subtract 500 from both sides to isolate x:", "[\n750 - 500 = x\n]", "[\nx = 250\n]", "---", "### Final Answer", "The solution is:", "[\n\boxed{x = 250}\n]", "This means 20% of (500 + 250) equals 150:", "[\n0.20 \ imes 750 = 150\n]", "---", "### Why This Skill Matters", "Mastering equations like this builds fluency in algebra—the backbone of many STEM fields, financial literacy, and logical reasoning. Practice solving such problems regularly to strengthen your ability to model real-life scenarios mathematically.", "---", "### Tips for Quick Problem Solving", "- Always identify knowns and unknowns clearly.\n- Simplify for easier computation (e.g., convert 20% to 0.20).\n- Use inverse operations to isolate variables.\n- Verify your answer by plugging it back into the original equation.", "---", "Conclusion", "Solving 150 = 0.20(500 + x) is a practical example of how algebra helps solve real-world problems. With clear steps—dividing to isolate the variable and then simplifying—this equation becomes accessible and empowering. Keep practicing, and soon, equations like this won’t be tricky—they’ll be simple and satisfying.", "---", "Keywords for SEO Optimization:\nalgebra equation solving, how to solve 150 = 0.20(500 + x), step-by-step equation solving guide, solve linear equations, algebraic word problems, 20% problem solving, mathematics tutoring, middle school math help, essential algebra skills."]