Solve -2x+3(x-3)+x-1/2=x+1/3-x+3/6

$$- 2 x + 3 ( x - 3 ) + \frac { x - 1 } { 2 } = \frac { x + 1 } { 3 } - \frac { x + 3 } { 6 }$$

Solve for x

$$x=7$$

Steps for Solving Linear Equation

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

$$-12x+18\left(x-3\right)+3\left(x-1\right)=2\left(x+1\right)-\left(x+3\right)$$

Use the distributive property to multiply 18 by x-3.

$$-12x+18x-54+3\left(x-1\right)=2\left(x+1\right)-\left(x+3\right)$$

Combine -12x and 18x to get 6x.

$$6x-54+3\left(x-1\right)=2\left(x+1\right)-\left(x+3\right)$$

Use the distributive property to multiply 3 by x-1.

$$6x-54+3x-3=2\left(x+1\right)-\left(x+3\right)$$

Combine 6x and 3x to get 9x.

$$9x-54-3=2\left(x+1\right)-\left(x+3\right)$$

Subtract 3 from -54 to get -57.

$$9x-57=2\left(x+1\right)-\left(x+3\right)$$

Use the distributive property to multiply 2 by x+1.

$$9x-57=2x+2-\left(x+3\right)$$

To find the opposite of x+3, find the opposite of each term.

$$9x-57=2x+2-x-3$$

Combine 2x and -x to get x.

$$9x-57=x+2-3$$

Subtract 3 from 2 to get -1.

$$9x-57=x-1$$

Subtract x from both sides.

$$9x-57-x=-1$$

Combine 9x and -x to get 8x.

$$8x-57=-1$$

Add 57 to both sides.

$$8x=-1+57$$

Add -1 and 57 to get 56.

$$8x=56$$

Divide both sides by 8.

$$x=\frac{56}{8}$$

Divide 56 by 8 to get 7.

$$x=7$$