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Solve x−52\frac{x - 5}{2} equals x+26\frac{x + 2}{6} minus 33.

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Full solution

Q. Solve x−52\frac{x - 5}{2} equals x+26\frac{x + 2}{6} minus 33.
  1. Find Common Denominator: Find a common denominator to combine the fractions on the right side of the equation.\newline(6)(x−52)=(2)(x+26)−(6)(3)(6)\left(\frac{x - 5}{2}\right) = (2)\left(\frac{x + 2}{6}\right) - (6)(3)
  2. Simplify by Multiplying: Simplify the equation by multiplying each term by the common denominator. 3(x−5)=(x+2)−183(x - 5) = (x + 2) - 18
  3. Distribute and Simplify: Distribute the 33 on the left side and simplify the right side.3x−15=x+2−183x - 15 = x + 2 - 18
  4. Combine Like Terms: Combine like terms on the right side.\newline3x−15=x−163x - 15 = x - 16
  5. Subtract xx Terms: Subtract xx from both sides to get the xx terms on one side.\newline3x−x−15=x−x−163x - x - 15 = x - x - 16
  6. Isolate xx Term: Simplify both sides of the equation.2x−15=−162x - 15 = -16
  7. Add to Isolate xx: Add 1515 to both sides to isolate the xx term.\newline2x−15+15=−16+152x - 15 + 15 = -16 + 15
  8. Divide to Solve for x: Simplify both sides of the equation. 2x=−12x = -1
  9. Divide to Solve for xx: Simplify both sides of the equation.2x=−12x = -1Divide both sides by 22 to solve for xx.x=−12x = -\frac{1}{2}

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