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

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

Solve for x

$$x = \frac{29}{13} = 2\frac{3}{13} \approx 2.230769231$$

Steps for Solving Linear Equation

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

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

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

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

Combine 6x and 3x to get 9x.

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

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

$$9x-9=18-4x+2$$

Add 18 and 2 to get 20.

$$9x-9=20-4x$$

Add 4x to both sides.

$$9x-9+4x=20$$

Combine 9x and 4x to get 13x.

$$13x-9=20$$

Add 9 to both sides.

$$13x=20+9$$

Add 20 and 9 to get 29.

$$13x=29$$

Divide both sides by 13.

$$x=\frac{29}{13}$$