Solve x/3-x-1/2=x-13/9

$$\frac { x } { 3 } - \frac { x - 1 } { 2 } = \frac { x - 13 } { 9 }$$

Solve for x

$$x=7$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 18, the least common multiple of 3,2,9.

$$6x-9\left(x-1\right)=2\left(x-13\right)$$

Use the distributive property to multiply -9 by x-1.

$$6x-9x+9=2\left(x-13\right)$$

Combine 6x and -9x to get -3x.

$$-3x+9=2\left(x-13\right)$$

Use the distributive property to multiply 2 by x-13.

$$-3x+9=2x-26$$

Subtract 2x from both sides.

$$-3x+9-2x=-26$$

Combine -3x and -2x to get -5x.

$$-5x+9=-26$$

Subtract 9 from both sides.

$$-5x=-26-9$$

Subtract 9 from -26 to get -35.

$$-5x=-35$$

Divide both sides by -5.

$$x=\frac{-35}{-5}$$

Divide -35 by -5 to get 7.

$$x=7$$