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

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

Solve for x

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

Steps for Solving Linear Equation

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

$$6+18\left(\frac{x}{2}-1\right)=12\left(x-1\right)+2-6x$$

Use the distributive property to multiply 18 by \frac{x}{2}-1.

$$6+18\times \frac{x}{2}-18=12\left(x-1\right)+2-6x$$

Cancel out 2, the greatest common factor in 18 and 2.

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

Subtract 18 from 6 to get -12.

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

Use the distributive property to multiply 12 by x-1.

$$-12+9x=12x-12+2-6x$$

Add -12 and 2 to get -10.

$$-12+9x=12x-10-6x$$

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

$$-12+9x=6x-10$$

Subtract 6x from both sides.

$$-12+9x-6x=-10$$

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

$$-12+3x=-10$$

Add 12 to both sides.

$$3x=-10+12$$

Add -10 and 12 to get 2.

$$3x=2$$

Divide both sides by 3.

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