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Solve for 
x.

(-5)/(3)+(x-1)/(6)=x-6
Answer:

Solve for x \mathrm{x} .\newline53+x16=x6 \frac{-5}{3}+\frac{x-1}{6}=x-6 \newlineAnswer:

Full solution

Q. Solve for x \mathrm{x} .\newline53+x16=x6 \frac{-5}{3}+\frac{x-1}{6}=x-6 \newlineAnswer:
  1. Identify Equation: Identify the equation to solve for xx. The equation given is 53+x16=x6\frac{-5}{3} + \frac{x-1}{6} = x - 6.
  2. Find Common Denominator: Find a common denominator for the fractions on the left side of the equation.\newlineThe common denominator for 33 and 66 is 66. We will multiply the terms by the appropriate factors to get rid of the denominators.
  3. Multiply by Common Denominator: Multiply the entire equation by the common denominator to clear the fractions.\newlineMultiplying each term by 66 gives us:\newline6×53+6×x16=6×(x6)6 \times \frac{-5}{3} + 6 \times \frac{x-1}{6} = 6 \times (x - 6)
  4. Simplify Equation: Simplify the equation.\newlineSimplifying each term, we get:\newline10+(x1)=6x36-10 + (x - 1) = 6x - 36
  5. Distribute and Combine: Distribute and combine like terms.\newlineWe will distribute the 66 on the right side and combine like terms:\newline10+x1=6x36-10 + x - 1 = 6x - 36
  6. Simplify Left Side: Simplify the left side of the equation.\newlineCombining 10-10 and 1-1, we get:\newlinex11=6x36x - 11 = 6x - 36
  7. Move Terms: Move the xx terms to one side and the constant terms to the other side.\newlineSubtract xx from both sides and add 3636 to both sides:\newlinex11x=6x36xx - 11 - x = 6x - 36 - x\newline3611=6xx36+3636 - 11 = 6x - x - 36 + 36
  8. Simplify Both Sides: Simplify both sides of the equation. 25=5x25 = 5x
  9. Solve for x: Solve for x.\newlineDivide both sides by 55 to isolate x:\newline255=5x5\frac{25}{5} = \frac{5x}{5}\newlinex=5x = 5

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