Solve 10-3x/8-x+2/9-17/36=3x-2/6

$$\frac{ 10-3x }{ 8 } - \frac{ x+2 }{ 9 } - \frac{ 17 }{ 36 } = \frac{ 3x-2 }{ 6 }$$

Solve for x

$$x=\frac{64}{71}\approx 0.901408451$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 72, the least common multiple of 8,9,36,6.

$$9\left(10-3x\right)-8\left(x+2\right)-34=12\left(3x-2\right)$$

Use the distributive property to multiply 9 by 10-3x.

$$90-27x-8\left(x+2\right)-34=12\left(3x-2\right)$$

Use the distributive property to multiply -8 by x+2.

$$90-27x-8x-16-34=12\left(3x-2\right)$$

Combine -27x and -8x to get -35x.

$$90-35x-16-34=12\left(3x-2\right)$$

Subtract 16 from 90 to get 74.

$$74-35x-34=12\left(3x-2\right)$$

Subtract 34 from 74 to get 40.

$$40-35x=12\left(3x-2\right)$$

Use the distributive property to multiply 12 by 3x-2.

$$40-35x=36x-24$$

Subtract 36x from both sides.

$$40-35x-36x=-24$$

Combine -35x and -36x to get -71x.

$$40-71x=-24$$

Subtract 40 from both sides.

$$-71x=-24-40$$

Subtract 40 from -24 to get -64.

$$-71x=-64$$

Divide both sides by -71.

$$x=\frac{-64}{-71}$$

Fraction \frac{-64}{-71} can be simplified to \frac{64}{71} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{64}{71}$$