Solve =2852x-1/2+2x+3/3=x+1/6-x-1/12+frac{3}{4}x

$$= 285 \frac { 2 x - 1 } { 2 } + \frac { 2 x + 3 } { 3 } = \frac { x + 1 } { 6 } - \frac { x - 1 } { 12 } + \frac { 3 } { 4 } x$$

Solve for x

$$x=\frac{1701}{3418}\approx 0.49765945$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 12, the least common multiple of 2,3,6,12,4.

$$1710\left(2x-1\right)+4\left(2x+3\right)=2\left(x+1\right)-\left(x-1\right)+9x$$

Use the distributive property to multiply 1710 by 2x-1.

$$3420x-1710+4\left(2x+3\right)=2\left(x+1\right)-\left(x-1\right)+9x$$

Use the distributive property to multiply 4 by 2x+3.

$$3420x-1710+8x+12=2\left(x+1\right)-\left(x-1\right)+9x$$

Combine 3420x and 8x to get 3428x.

$$3428x-1710+12=2\left(x+1\right)-\left(x-1\right)+9x$$

Add -1710 and 12 to get -1698.

$$3428x-1698=2\left(x+1\right)-\left(x-1\right)+9x$$

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

$$3428x-1698=2x+2-\left(x-1\right)+9x$$

To find the opposite of x-1, find the opposite of each term.

$$3428x-1698=2x+2-x-\left(-1\right)+9x$$

The opposite of -1 is 1.

$$3428x-1698=2x+2-x+1+9x$$

Combine 2x and -x to get x.

$$3428x-1698=x+2+1+9x$$

Add 2 and 1 to get 3.

$$3428x-1698=x+3+9x$$

Combine x and 9x to get 10x.

$$3428x-1698=10x+3$$

Subtract 10x from both sides.

$$3428x-1698-10x=3$$

Combine 3428x and -10x to get 3418x.

$$3418x-1698=3$$

Add 1698 to both sides.

$$3418x=3+1698$$

Add 3 and 1698 to get 1701.

$$3418x=1701$$

Divide both sides by 3418.

$$x=\frac{1701}{3418}$$