Solve 3*(x-2)/4+1/2x-x=x-1/2-2left(x+2right)/4+frac{1}{6}

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

Solve for x

$$x=\frac{2}{3}\approx 0.666666667$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 12, the least common multiple of 4,2,6.

$$3\times 3\left(x-2\right)+6x-12x=6\left(x-1\right)-3\times 2\left(x+2\right)+2$$

Multiply 3 and 3 to get 9.

$$9\left(x-2\right)+6x-12x=6\left(x-1\right)-3\times 2\left(x+2\right)+2$$

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

$$9x-18+6x-12x=6\left(x-1\right)-3\times 2\left(x+2\right)+2$$

Combine 9x and 6x to get 15x.

$$15x-18-12x=6\left(x-1\right)-3\times 2\left(x+2\right)+2$$

Combine 15x and -12x to get 3x.

$$3x-18=6\left(x-1\right)-3\times 2\left(x+2\right)+2$$

Use the distributive property to multiply 6 by x-1.

$$3x-18=6x-6-3\times 2\left(x+2\right)+2$$

Multiply -3 and 2 to get -6.

$$3x-18=6x-6-6\left(x+2\right)+2$$

Use the distributive property to multiply -6 by x+2.

$$3x-18=6x-6-6x-12+2$$

Combine 6x and -6x to get 0.

$$3x-18=-6-12+2$$

Subtract 12 from -6 to get -18.

$$3x-18=-18+2$$

Add -18 and 2 to get -16.

$$3x-18=-16$$

Add 18 to both sides.

$$3x=-16+18$$

Add -16 and 18 to get 2.

$$3x=2$$

Divide both sides by 3.

$$x=\frac{2}{3}$$