Solve x-4/6+2x-4/8=5x/10-5x-6/12

$$\frac { x - 4 } { 6 } + \frac { 2 x - 4 } { 8 } = \frac { 5 x } { 10 } - \frac { 5 x - 6 } { 12 }$$

Solve for x

$$x=5$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 120, the least common multiple of 6,8,10,12.

$$20\left(x-4\right)+15\left(2x-4\right)=12\times 5x-10\left(5x-6\right)$$

Use the distributive property to multiply 20 by x-4.

$$20x-80+15\left(2x-4\right)=12\times 5x-10\left(5x-6\right)$$

Use the distributive property to multiply 15 by 2x-4.

$$20x-80+30x-60=12\times 5x-10\left(5x-6\right)$$

Combine 20x and 30x to get 50x.

$$50x-80-60=12\times 5x-10\left(5x-6\right)$$

Subtract 60 from -80 to get -140.

$$50x-140=12\times 5x-10\left(5x-6\right)$$

Multiply 12 and 5 to get 60.

$$50x-140=60x-10\left(5x-6\right)$$

Use the distributive property to multiply -10 by 5x-6.

$$50x-140=60x-50x+60$$

Combine 60x and -50x to get 10x.

$$50x-140=10x+60$$

Subtract 10x from both sides.

$$50x-140-10x=60$$

Combine 50x and -10x to get 40x.

$$40x-140=60$$

Add 140 to both sides.

$$40x=60+140$$

Add 60 and 140 to get 200.

$$40x=200$$

Divide both sides by 40.

$$x=\frac{200}{40}$$

Divide 200 by 40 to get 5.

$$x=5$$