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

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

Solve for x

$$x=-4$$

Steps for Solving Linear Equation

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

$$3\left(x+1\right)+2\left(2x+1\right)-\left(3x+1\right)=-12$$

Use the distributive property to multiply 3 by x+1.

$$3x+3+2\left(2x+1\right)-\left(3x+1\right)=-12$$

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

$$3x+3+4x+2-\left(3x+1\right)=-12$$

Combine 3x and 4x to get 7x.

$$7x+3+2-\left(3x+1\right)=-12$$

Add 3 and 2 to get 5.

$$7x+5-\left(3x+1\right)=-12$$

To find the opposite of 3x+1, find the opposite of each term.

$$7x+5-3x-1=-12$$

Combine 7x and -3x to get 4x.

$$4x+5-1=-12$$

Subtract 1 from 5 to get 4.

$$4x+4=-12$$

Subtract 4 from both sides.

$$4x=-12-4$$

Subtract 4 from -12 to get -16.

$$4x=-16$$

Divide both sides by 4.

$$x=\frac{-16}{4}$$

Divide -16 by 4 to get -4.

$$x=-4$$