Solve x+3/4+2x+1/3=x-3/6+3x+1/12

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

Solve for x

$$x=-3$$

Steps for Solving Linear Equation

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

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

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

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

Use the distributive property to multiply 4 by 2x+1.

$$3x+9+8x+4=2\left(x-3\right)+3x+1$$

Combine 3x and 8x to get 11x.

$$11x+9+4=2\left(x-3\right)+3x+1$$

Add 9 and 4 to get 13.

$$11x+13=2\left(x-3\right)+3x+1$$

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

$$11x+13=2x-6+3x+1$$

Combine 2x and 3x to get 5x.

$$11x+13=5x-6+1$$

Add -6 and 1 to get -5.

$$11x+13=5x-5$$

Subtract 5x from both sides.

$$11x+13-5x=-5$$

Combine 11x and -5x to get 6x.

$$6x+13=-5$$

Subtract 13 from both sides.

$$6x=-5-13$$

Subtract 13 from -5 to get -18.

$$6x=-18$$

Divide both sides by 6.

$$x=\frac{-18}{6}$$

Divide -18 by 6 to get -3.

$$x=-3$$