Solving, \( 30 + x = 0.8(50 + x) \) → \( 30 + x = 40 + 0.8x \) → \( 0.2x = 10 \) → \( x = 50 \) liters.
["How to Solve the Equation ( 30 + x = 0.8(50 + x) ) – Step-by-Step Explanation", "Solving linear equations is a fundamental algebraic skill with real-world applications, from budgeting and science to engineering and finance. One commonly encountered equation is:", "[\n30 + x = 0.8(50 + x)\n]", "In this article, we’ll break down step-by-step how to solve this equation to find ( x = 50 ) liters (or units). Understanding this process helps simplify real-world problems involving percentages, costs, or proportions.", "---", "### Step 1: Write the Original Equation", "Start with the given equation:", "[\n30 + x = 0.8(50 + x)\n]", "This equation typically represents a balance of quantities—say, a cost equation where ( x ) is an unknown volume or quantity, and comparisons involve fixed values and scaling factors.", "---", "### Step 2: Expand the Right Side", "To eliminate the parentheses, apply the distributive property (( a(b + c) = ab + ac )) to the right-hand side:", "[\n30 + x = 0.8 \cdot 50 + 0.8x\n]", "Compute ( 0.8 \ imes 50 = 40 ), so:", "[\n30 + x = 40 + 0.8x\n]", "---", "### Step 3: Get All Variables on One Side", "Subtract ( 0.8x ) from both sides to collect variable terms:", "[\n30 + x - 0.8x = 40\n]", "Simplify:", "[\n30 + 0.2x = 40\n]", "This step isolates the terms with ( x ) on the left.", "---", "### Step 4: Isolate the Variable Term", "Subtract 30 from both sides:", "[\n0.2x = 10\n]", "This equation reveals how much ( x ) contributes to the final result.", "---", "### Step 5: Solve for ( x )", "Divide both sides by 0.2:", "[\nx = \frac{10}{0.2} = 50\n]", "So, ( x = 50 ) liters (or the unit of measurement in your problem).", "---", "### Real-World Interpretation", "This equation might model, for example:", "- A scenario where ( x ) is a volume of a liquid at 30 liters, and ( 0.8(50 + x) ) represents a material that fills 80% of an additional 50 liters.\n- Solving gives ( x = 50 ) liters—meaning you start with 30 liters and add 50 liters under scaled conditions.", "---", "### Key Takeaways", "- Distribute carefully to expand parentheses.\n- Combine like terms to isolate variables.\n- Isolate ( x ) using inverse operations.\n- Divide to find the exact value.", "---", "### Conclusion", "Mastering these steps allows quick, accurate solutions to linear equations commonly found in algebra, physics, chemistry, and economics. Remember, every equation tells a story—solving it reveals the unknown, turning abstract symbols into practical answers.", "Tip: Practice with similar equations involving percentages and mixed expressions to strengthen your algebraic fluency!", "---", "Keywords:\nSolve ( 30 + x = 0.8(50 + x) ), linear equation solving steps, algebraic problem solving, beginner algebra tutorial, how to isolate x, equation chain steps, apply distributive property, solve for x, real-world math applications, algebra skills practice", "Meta Description:\nLearn step-by-step how to solve ( 30 + x = 0.8(50 + x) ), arriving at ( x = 50 ) liters. Master linear equations with practical examples and instant downloading of skills."]
