Solve 2(3x-8)/9-5(x-3)/3=3(x-8)/4+17/36

$$\frac{ 2(3x-8) }{ 9 } - \frac{ 5(x-3) }{ 3 } = \frac{ 3(x-8) }{ 4 } + \frac{ 17 }{ 36 }$$

Solve for x

$$x=5$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 36, the least common multiple of 9,3,4,36.

$$4\times 2\left(3x-8\right)-12\times 5\left(x-3\right)=9\times 3\left(x-8\right)+17$$

Multiply 4 and 2 to get 8.

$$8\left(3x-8\right)-12\times 5\left(x-3\right)=9\times 3\left(x-8\right)+17$$

Use the distributive property to multiply 8 by 3x-8.

$$24x-64-12\times 5\left(x-3\right)=9\times 3\left(x-8\right)+17$$

Multiply -12 and 5 to get -60.

$$24x-64-60\left(x-3\right)=9\times 3\left(x-8\right)+17$$

Use the distributive property to multiply -60 by x-3.

$$24x-64-60x+180=9\times 3\left(x-8\right)+17$$

Combine 24x and -60x to get -36x.

$$-36x-64+180=9\times 3\left(x-8\right)+17$$

Add -64 and 180 to get 116.

$$-36x+116=9\times 3\left(x-8\right)+17$$

Multiply 9 and 3 to get 27.

$$-36x+116=27\left(x-8\right)+17$$

Use the distributive property to multiply 27 by x-8.

$$-36x+116=27x-216+17$$

Add -216 and 17 to get -199.

$$-36x+116=27x-199$$

Subtract 27x from both sides.

$$-36x+116-27x=-199$$

Combine -36x and -27x to get -63x.

$$-63x+116=-199$$

Subtract 116 from both sides.

$$-63x=-199-116$$

Subtract 116 from -199 to get -315.

$$-63x=-315$$

Divide both sides by -63.

$$x=\frac{-315}{-63}$$

Divide -315 by -63 to get 5.

$$x=5$$