Solve x+1/3-2-1/2=-x/6+5/2

$$\frac { x + 1 } { 3 } - \frac { 2 - 1 } { 2 } = \frac { - x } { 6 } + \frac { 5 } { 2 }$$

Solve for x

$$x = \frac{16}{3} = 5\frac{1}{3} \approx 5.333333333$$

Steps for Solving Linear Equation

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

$$2\left(x+1\right)-3\left(2-1\right)=-x+15$$

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

$$2x+2-3\left(2-1\right)=-x+15$$

Subtract 1 from 2 to get 1.

$$2x+2-3=-x+15$$

Subtract 3 from 2 to get -1.

$$2x-1=-x+15$$

Add x to both sides.

$$2x-1+x=15$$

Combine 2x and x to get 3x.

$$3x-1=15$$

Add 1 to both sides.

$$3x=15+1$$

Add 15 and 1 to get 16.

$$3x=16$$

Divide both sides by 3.

$$x=\frac{16}{3}$$