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

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

Solve for x

$$x = \frac{295}{7} = 42\frac{1}{7} \approx 42.142857143$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 60, the least common multiple of 3,5,4.

$$20\left(2x-2\right)-360=12\left(4x-5\right)-15\left(x+3\right)$$

Use the distributive property to multiply 20 by 2x-2.

$$40x-40-360=12\left(4x-5\right)-15\left(x+3\right)$$

Subtract 360 from -40 to get -400.

$$40x-400=12\left(4x-5\right)-15\left(x+3\right)$$

Use the distributive property to multiply 12 by 4x-5.

$$40x-400=48x-60-15\left(x+3\right)$$

Use the distributive property to multiply -15 by x+3.

$$40x-400=48x-60-15x-45$$

Combine 48x and -15x to get 33x.

$$40x-400=33x-60-45$$

Subtract 45 from -60 to get -105.

$$40x-400=33x-105$$

Subtract 33x from both sides.

$$40x-400-33x=-105$$

Combine 40x and -33x to get 7x.

$$7x-400=-105$$

Add 400 to both sides.

$$7x=-105+400$$

Add -105 and 400 to get 295.

$$7x=295$$

Divide both sides by 7.

$$x=\frac{295}{7}$$