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

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

Solve for x

$$x=2$$

Steps for Solving Linear Equation

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

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

To find the opposite of x+2, find the opposite of each term.

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

Combine 6x and -x to get 5x.

$$5x-2+6=3\left(2x-1\right)-2x+3\times 3\left(x-1\right)$$

Add -2 and 6 to get 4.

$$5x+4=3\left(2x-1\right)-2x+3\times 3\left(x-1\right)$$

Use the distributive property to multiply 3 by 2x-1.

$$5x+4=6x-3-2x+3\times 3\left(x-1\right)$$

Combine 6x and -2x to get 4x.

$$5x+4=4x-3+3\times 3\left(x-1\right)$$

Multiply 3 and 3 to get 9.

$$5x+4=4x-3+9\left(x-1\right)$$

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

$$5x+4=4x-3+9x-9$$

Combine 4x and 9x to get 13x.

$$5x+4=13x-3-9$$

Subtract 9 from -3 to get -12.

$$5x+4=13x-12$$

Subtract 13x from both sides.

$$5x+4-13x=-12$$

Combine 5x and -13x to get -8x.

$$-8x+4=-12$$

Subtract 4 from both sides.

$$-8x=-12-4$$

Subtract 4 from -12 to get -16.

$$-8x=-16$$

Divide both sides by -8.

$$x=\frac{-16}{-8}$$

Divide -16 by -8 to get 2.

$$x=2$$