Solve 3x+6/12+2x-2/6=5x+10/4-x+4/2

$$\frac { 3 x + 6 } { 12 } + \frac { 2 x - 2 } { 6 } = \frac { 5 x + 10 } { 4 } - \frac { x + 4 } { 2 }$$

Solve for x

$$x=-2$$

Steps for Solving Linear Equation

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

$$3x+6+2\left(2x-2\right)=3\left(5x+10\right)-6\left(x+4\right)$$

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

$$3x+6+4x-4=3\left(5x+10\right)-6\left(x+4\right)$$

Combine 3x and 4x to get 7x.

$$7x+6-4=3\left(5x+10\right)-6\left(x+4\right)$$

Subtract 4 from 6 to get 2.

$$7x+2=3\left(5x+10\right)-6\left(x+4\right)$$

Use the distributive property to multiply 3 by 5x+10.

$$7x+2=15x+30-6\left(x+4\right)$$

Use the distributive property to multiply -6 by x+4.

$$7x+2=15x+30-6x-24$$

Combine 15x and -6x to get 9x.

$$7x+2=9x+30-24$$

Subtract 24 from 30 to get 6.

$$7x+2=9x+6$$

Subtract 9x from both sides.

$$7x+2-9x=6$$

Combine 7x and -9x to get -2x.

$$-2x+2=6$$

Subtract 2 from both sides.

$$-2x=6-2$$

Subtract 2 from 6 to get 4.

$$-2x=4$$

Divide both sides by -2.

$$x=\frac{4}{-2}$$

Divide 4 by -2 to get -2.

$$x=-2$$