Correct setup: \( 20x + 35(150 - x) = 4000 \), solve again:
["Correct Setup and Solution of the Equation ( 20x + 35(150 - x) = 4000 )", "When solving linear equations, proper setup is essential for accuracy and clarity. Consider the equation:", "[\n20x + 35(150 - x) = 4000\n]", "### Correct Setup Explained", "1. Distribute and Expand\nTo eliminate parentheses, first distribute ( 35 ) across ( (150 - x) ):", "[\n20x + 35 \cdot 150 - 35x = 4000\n]", "This simplifies to:", "[\n20x + 5250 - 35x = 4000\n]", "2. Combine Like Terms\nCombine the ( x )-terms:", "[\n(20x - 35x) + 5250 = 4000\n]\n[\n-15x + 5250 = 4000\n]", "3. Isolate the Variable\nSubtract 5250 from both sides:", "[\n-15x = 4000 - 5250\n]\n[\n-15x = -1250\n]", "4. Solve for ( x )\nDivide both sides by (-15):", "[\nx = \frac{-1250}{-15} = \frac{1250}{15} = \frac{250}{3} \approx 83.33\n]", "### Final Solution\nThe correct solution to the equation ( 20x + 35(150 - x) = 4000 ) is:", "[\nx = \frac{250}{3}\n]", "---", "### Why This Setup Works", "- Proper distribution prevents mistakes in coefficient handling.\n- Combining like terms simplifies the expression methodically.\n- Isolation of the variable ensures a clear path to isolating ( x ).\n- Segmenting each step allows verification and reduces error risk.", "This structured approach ensures accuracy, especially in algebraic equations with nested expressions. Use it when solving similar linear equations involving parentheses and variables on both sides."]
