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Solve the following equation for x. Express your answer in the simplest form. 3(9x-7)-1=4x+6(-x+7)

Solve the following equation for x x . Express your answer in the simplest form.\newline3(9x−7)−1=4x+6(−x+7) 3(9 x-7)-1=4 x+6(-x+7) \newline

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Full solution

Q. Solve the following equation for x x . Express your answer in the simplest form.\newline3(9x−7)−1=4x+6(−x+7) 3(9 x-7)-1=4 x+6(-x+7) \newline
  1. Expand left side: Expand the left side: 3(9x−7)−1=27x−21−13(9x - 7) - 1 = 27x - 21 - 1.
  2. Combine like terms (left): Combine like terms on the left side: 27x−21−1=27x−2227x - 21 - 1 = 27x - 22.
  3. Expand right side: Expand the right side: 4x+6(−x+7)=4x−6x+424x + 6(-x + 7) = 4x - 6x + 42.
  4. Combine like terms (right): Combine like terms on the right side: 4x−6x+42=−2x+424x - 6x + 42 = -2x + 42.
  5. Set equation equal: Set the equation with both sides equal to each other: 27x−22=−2x+4227x - 22 = -2x + 42.
  6. Add xx terms: Add 2x2x to both sides to get all xx terms on one side: 27x+2x−22=4227x + 2x - 22 = 42.
  7. Combine like terms: Combine like terms: 29x−22=4229x - 22 = 42.
  8. Add to isolate xx: Add 2222 to both sides to isolate the xx term: 29x=42+2229x = 42 + 22.
  9. Combine like terms: Combine like terms: 29x=6429x = 64.
  10. Divide to solve xx: Divide both sides by 2929 to solve for xx: x=6429x = \frac{64}{29}.

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