Solve 3(x-4)/2-x/6+x/2=x-9/3

$$\frac { 3 ( x - 4 ) } { 2 } - \frac { x } { 6 } + \frac { x } { 2 } = \frac { x - 9 } { 3 }$$

Solve for x

$$x=2$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 6, the least common multiple of 2,6,3.

$$3\times 3\left(x-4\right)-x+3x=2\left(x-9\right)$$

Multiply 3 and 3 to get 9.

$$9\left(x-4\right)-x+3x=2\left(x-9\right)$$

Use the distributive property to multiply 9 by x-4.

$$9x-36-x+3x=2\left(x-9\right)$$

Combine 9x and 3x to get 12x.

$$12x-36-x=2\left(x-9\right)$$

Use the distributive property to multiply 2 by x-9.

$$12x-36-x=2x-18$$

Subtract 2x from both sides.

$$12x-36-x-2x=-18$$

Combine 12x and -2x to get 10x.

$$10x-36-x=-18$$

Add 36 to both sides.

$$10x-x=-18+36$$

Add -18 and 36 to get 18.

$$10x-x=18$$

Combine 10x and -x to get 9x.

$$9x=18$$

Divide both sides by 9.

$$x=\frac{18}{9}$$

Divide 18 by 9 to get 2.

$$x=2$$