Solve 2x-1/2-11/3=31/3-x+1/3

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

Solve for x

$$x = \frac{29}{8} = 3\frac{5}{8} = 3.625$$

Steps for Solving Linear Equation

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

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

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

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

Add 3 and 1 to get 4.

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

Multiply -2 and 4 to get -8.

$$6x-3-8=2\left(3\times 3+1\right)-2\left(x+1\right)$$

Subtract 8 from -3 to get -11.

$$6x-11=2\left(3\times 3+1\right)-2\left(x+1\right)$$

Multiply 3 and 3 to get 9.

$$6x-11=2\left(9+1\right)-2\left(x+1\right)$$

Add 9 and 1 to get 10.

$$6x-11=2\times 10-2\left(x+1\right)$$

Multiply 2 and 10 to get 20.

$$6x-11=20-2\left(x+1\right)$$

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

$$6x-11=20-2x-2$$

Subtract 2 from 20 to get 18.

$$6x-11=18-2x$$

Add 2x to both sides.

$$6x-11+2x=18$$

Combine 6x and 2x to get 8x.

$$8x-11=18$$

Add 11 to both sides.

$$8x=18+11$$

Add 18 and 11 to get 29.

$$8x=29$$

Divide both sides by 8.

$$x=\frac{29}{8}$$