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

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

Solve for x

$$x=8$$

Steps for Solving Linear Equation

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

$$6x+4x=3\times 3x+2\times 5x-72$$

Combine 6x and 4x to get 10x.

$$10x=3\times 3x+2\times 5x-72$$

Multiply 3 and 3 to get 9. Multiply 2 and 5 to get 10.

$$10x=9x+10x-72$$

Combine 9x and 10x to get 19x.

$$10x=19x-72$$

Subtract 19x from both sides.

$$10x-19x=-72$$

Combine 10x and -19x to get -9x.

$$-9x=-72$$

Divide both sides by -9.

$$x=\frac{-72}{-9}$$

Divide -72 by -9 to get 8.

$$x=8$$