La concentration en alcool devient \( \frac{4}{10 + x} = 0.25 \).

["SEO Article: How to Solve the Equation ( \frac{4}{10 + x} = 0.25 ) – Step-by-Step Guide", "---\nTitle: Solve ( \frac{4}{10 + x} = 0.25 ) – Easy Algebra Solution with Explanation", "---", "Are you struggling with solving rational equations like ( \frac{4}{10 + x} = 0.25 )? This article provides a clear, step-by-step guide to solve this equation, which is commonly encountered in algebra and foundational math courses. Whether you're learning for school, test prep, or personal growth, mastering this concept helps strengthen your algebraic skills.", "In this guide, we’ll break down how to isolate ( x ) and verify the solution, explaining each step in simple terms. Plus, we’ll show how such equations appear in real-life applications like concentration calculations.", "---", "### Problem Statement", "Solve for ( x ):", "[\n\frac{4}{10 + x} = 0.25\n]", "This equation expresses a concentration or ratio problem—where 4 units of a substance are proportional to a fraction of a total volume depending on ( x ).", "---", "### Step 1: Understand the Equation", "The expression ( \frac{4}{10 + x} ) models a concentration where the numerator (4) represents a fixed quantity (e.g., grams of alcohol), and the denominator ( 10 + x ) represents total volume or denominator quantity dependent on variable ( x ). The equation states that this concentration equals 0.25 (or 25%).", "---", "### Step 2: Eliminate the Fraction", "To simplify, multiply both sides by ( 10 + x ):", "[\n4 = 0.25 \ imes (10 + x)\n]", "This step removes the denominator, making the equation easier to solve.", "---", "### Step 3: Solve for the Denominator", "Now divide both sides by 0.25:", "[\n\frac{4}{0.25} = 10 + x\n]", "Since ( \frac{4}{0.25} = 16 ), we get:", "[\n16 = 10 + x\n]", "---", "### Step 4: Isolate ( x )", "Subtract 10 from both sides:", "[\nx = 16 - 10 = 6\n]", "---", "### Step 5: Check the Solution", "Plug ( x = 6 ) back into the original equation:", "[\n\frac{4}{10 + 6} = \frac{4}{16} = 0.25\n]", "✅ The left side matches the right side, confirming the solution is correct.", "---", "### Final Answer", "[\n\boxed{x = 6}\n]", "---", "### Why This Equation Matters", "Equations of this form often appear in chemistry, finance, and physics—for example, calculating required concentrations, break-even points, or proportional relationships. Solving such equations builds a strong foundation for more complex mathematical models.", "---", "### Summary", "- Original equation: ( \frac{4}{10 + x} = 0.25 )\n- Step 1: Multiply both sides by ( 10 + x )\n- Step 2: Divide by 0.25 to isolate the denominator\n- Step 3: Solve for ( x ): ( x = 6 )\n- Verification: Confirmed ( x = 6 ) satisfies the original equation", "---", "### Try It Yourself!", "Need more practice? Try solving similar equations like ( \frac{5}{20 + x} = \frac{1}{4} ) or ( \frac{3}{5 + x} = 0.15 ). Understanding these patterns will boost your algebra confidence fast.", "---", "Keywords: solve ( \frac{4}{10 + x} = 0.25 ), algebra equation steps, rational equation solution, concentration equation, step-by-step algebra, how to solve fractional equations, solve ( \frac{4}{10 + x} = 0.25 )", "Meta Description: Learn how to solve ( \frac{4}{10 + x} = 0.25 ) with clear steps, verification, and real-world applications. Master this key algebra problem today!", "---", "Ready to deepen your math fluency? Explore related topics like solving linear equations, rational expressions, and concentration calculations.", "---", "Elevate your algebra skills—episode one: mastering fractions in equations!"]