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

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

Solve for x

$$x=17$$

Steps for Solving Linear Equation

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

$$36-3\left(x-1\right)=3\left(3-x\right)+2\left(x-2\right)$$

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

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

Add 36 and 3 to get 39.

$$39-3x=3\left(3-x\right)+2\left(x-2\right)$$

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

$$39-3x=9-3x+2\left(x-2\right)$$

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

$$39-3x=9-3x+2x-4$$

Combine -3x and 2x to get -x.

$$39-3x=9-x-4$$

Subtract 4 from 9 to get 5.

$$39-3x=5-x$$

Add x to both sides.

$$39-3x+x=5$$

Combine -3x and x to get -2x.

$$39-2x=5$$

Subtract 39 from both sides.

$$-2x=5-39$$

Subtract 39 from 5 to get -34.

$$-2x=-34$$

Divide both sides by -2.

$$x=\frac{-34}{-2}$$

Divide -34 by -2 to get 17.

$$x=17$$