Solve for: x/6-(x-2)/2 =(x-13)/9

Expression: $\frac{x}{6}-\frac{x-2}{2}=\frac{x-13}{9}$

Multiply by LCM

$3x-9(x-2)=2(x-13)$

Expand $ -9(x-2):{\quad}-9x+18$

$3x-9x+18=2(x-13)$

Add similar elements: $ 3x-9x=-6x$

$-6x+18=2(x-13)$

Expand $2(x-13):{\quad}2x-26$

$-6x+18=2x-26$

Subtract $18$ from both sides

$-6x+18-18=2x-26-18$

Simplify

$-6x=2x-44$

Subtract $2x$ from both sides

$-6x-2x=2x-44-2x$

Simplify

$-8x=-44$

Divide both sides by $-8$

$\frac{-8x}{-8}=\frac{-44}{-8}$

Simplify

$x=\frac{11}{2}$