Equation: \(0.4 \times 100 + 0.7 \times x = 0.5 \times (100 + x)\).
["Equation Solved: How to Solve (0.4 \ imes 100 + 0.7 \ imes x = 0.5 \ imes (100 + x))", "Solving equations is a foundational skill in algebra, and mastering them unlocks stronger problem-solving abilities. Today, we dive into a common yet insightful equation:", "[\n0.4 \ imes 100 + 0.7 \ imes x = 0.5 \ imes (100 + x)\n]", "Whether you’re a student learning algebra or a professional tackling real-world math challenges, understanding how to approach this equation is essential. Let’s break it down step by step.", "---", "### Step 1: Simplify Both Sides", "Start by simplifying the constant terms and expressions inside parentheses.", "Left side:\n[\n0.4 \ imes 100 = 40\n]\nSo, left side becomes:\n[\n40 + 0.7x\n]", "Right side:\n[\n0.5 \ imes (100 + x) = 0.5 \ imes 100 + 0.5 \ imes x = 50 + 0.5x\n]", "Now, the equation looks like:\n[\n40 + 0.7x = 50 + 0.5x\n]", "---", "### Step 2: Isolate Variable Terms", "Subtract (0.5x) from both sides to group the variable (x) terms:\n[\n40 + 0.7x - 0.5x = 50\n\Rightarrow 40 + 0.2x = 50\n]", "---", "### Step 3: Solve for (x)", "Now subtract 40 from both sides:\n[\n0.2x = 10\n]", "Then divide both sides by 0.2 to find (x):\n[\nx = \frac{10}{0.2} = 50\n]", "---", "### Final Answer:\n[\nx = 50\n]", "---", "### Why This Equation Matters", "This type of linear equation models real-life situations such as:", "- Calculating break-even points in economics\n- Solving proportions in chemistry or physics\n- Analyzing rates of change in data science and engineering", "Understanding how to manipulate variables and constants builds confidence in manipulating algebraic expressions—key for advanced math fields like calculus, linear algebra, and beyond.", "---", "### Pro Tips to Solve Similar Equations", "1. Simplify step-by-step — Never skip expanding parentheses or combining constants.\n2. Group like terms — Always isolate (x) terms on one side and constants on the other.\n3. Use inverse operations — Undo addition with subtraction and multiplication with division.\n4. Check your solution — Plug (x = 50) back into the original equation to confirm correctness.", "---", "### Conclusion", "Mastering equations like\n[\n0.4 \ imes 100 + 0.7x = 0.5 \ imes (100 + x)\n]\nnot only helps solve math problems effectively but strengthens logical reasoning across countless disciplines. With practice, algebraic manipulation becomes intuitive—and empowering.", "If you’re ready to tackle more equations, visit our full algebra guide and explore step-by-step tutorials designed to build your confidence and skill.", "---", "Keywords: algebra, solving equations, linear equations, equation solving, step-by-step math, equation tutorial, algebra problem solving, x value, real-world math equations."]
