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Solve for x. {:[(5x-5)/(x-2)=(1)/(3)],[x=]:}

Solve for x x .\newline5x−5x−2=13x= \begin{array}{l} \frac{5 x-5}{x-2}=\frac{1}{3} \\ x= \end{array}

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Full solution

Q. Solve for x x .\newline5x−5x−2=13x= \begin{array}{l} \frac{5 x-5}{x-2}=\frac{1}{3} \\ x= \end{array}
  1. Write down the system: Write down the given system of equations.\newlineWe have the system:\newline5x−5x−2=13x=x \begin{align*} \frac{5x-5}{x-2} &= \frac{1}{3} \\ x &= x \end{align*} \newlineThe second equation is redundant since it states that x equals itself. We will focus on the first equation to find the value of x.
  2. Cross-multiply to eliminate fractions: Cross-multiply to eliminate the fractions.\newline3(5x−5)=1(x−2) 3(5x - 5) = 1(x - 2)
  3. Distribute the numbers: Distribute the numbers on both sides of the equation.\newline15x−15=x−2 15x - 15 = x - 2
  4. Move terms and constants: Move all terms involving x to one side and constant terms to the other side.\newline15x−x=−2+15 15x - x = -2 + 15
  5. Simplify the equation: Simplify both sides of the equation.\newline14x=13 14x = 13
  6. Divide to solve for x: Divide both sides by 1414 to solve for x.\newlinex=1314 x = \frac{13}{14}

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