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Solve for x. (x-1)/(8)-(x-3)/(10)=(7)/(40) Answer:

Solve for x \mathrm{x} .\newlinex−18−x−310=740 \frac{x-1}{8}-\frac{x-3}{10}=\frac{7}{40} \newlineAnswer:

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Q. Solve for x \mathrm{x} .\newlinex−18−x−310=740 \frac{x-1}{8}-\frac{x-3}{10}=\frac{7}{40} \newlineAnswer:
  1. Find Common Denominator: Find a common denominator for the fractions to combine them.\newlineThe common denominator for 88, 1010, and 4040 is 4040.\newlineMultiply each term by 401\frac{40}{1} to clear the denominators.\newline(401)⋅(x−18)−(401)⋅(x−310)=(401)⋅(740)(\frac{40}{1}) \cdot (\frac{x-1}{8}) - (\frac{40}{1}) \cdot (\frac{x-3}{10}) = (\frac{40}{1}) \cdot (\frac{7}{40})
  2. Multiply by Common Denominator: Simplify each term.\newline(408)×(x−1)−(4010)×(x−3)=(4040)×7(\frac{40}{8}) \times (x-1) - (\frac{40}{10}) \times (x-3) = (\frac{40}{40}) \times 7\newline5(x−1)−4(x−3)=75(x-1) - 4(x-3) = 7
  3. Simplify Terms: Distribute the coefficients inside the parentheses. 5x−5−4x+12=75x - 5 - 4x + 12 = 7
  4. Distribute Coefficients: Combine like terms.\newline5x−4x−5+12=75x - 4x - 5 + 12 = 7\newlinex+7=7x + 7 = 7
  5. Combine Like Terms: Isolate the variable xx. \newlinex+7−7=7−7x + 7 - 7 = 7 - 7\newlinex=0x = 0

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