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

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

Solve for x

$$x=40$$

Steps for Solving Linear Equation

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

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

Use the distributive property to multiply 3 by 3x-6.

$$9x-18-6\left(x+5\right)=2\left(x-4\right)$$

Use the distributive property to multiply -6 by x+5.

$$9x-18-6x-30=2\left(x-4\right)$$

Combine 9x and -6x to get 3x.

$$3x-18-30=2\left(x-4\right)$$

Subtract 30 from -18 to get -48.

$$3x-48=2\left(x-4\right)$$

Use the distributive property to multiply 2 by x-4.

$$3x-48=2x-8$$

Subtract 2x from both sides.

$$3x-48-2x=-8$$

Combine 3x and -2x to get x.

$$x-48=-8$$

Add 48 to both sides.

$$x=-8+48$$

Add -8 and 48 to get 40.

$$x=40$$