Solve 3x-6/2-5x-7/9=4x-5/3-x+3/4-frac{1}{2}

$$\frac { 3 x - 6 } { 2 } - \frac { 5 x - 7 } { 9 } = \frac { 4 x - 5 } { 3 } - \frac { x + 3 } { 4 } - \frac { 1 } { 2 }$$

Solve for x

$$x=5$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 36, the least common multiple of 2,9,3,4.

$$18\left(3x-6\right)-4\left(5x-7\right)=12\left(4x-5\right)-9\left(x+3\right)-18$$

Use the distributive property to multiply 18 by 3x-6.

$$54x-108-4\left(5x-7\right)=12\left(4x-5\right)-9\left(x+3\right)-18$$

Use the distributive property to multiply -4 by 5x-7.

$$54x-108-20x+28=12\left(4x-5\right)-9\left(x+3\right)-18$$

Combine 54x and -20x to get 34x.

$$34x-108+28=12\left(4x-5\right)-9\left(x+3\right)-18$$

Add -108 and 28 to get -80.

$$34x-80=12\left(4x-5\right)-9\left(x+3\right)-18$$

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

$$34x-80=48x-60-9\left(x+3\right)-18$$

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

$$34x-80=48x-60-9x-27-18$$

Combine 48x and -9x to get 39x.

$$34x-80=39x-60-27-18$$

Subtract 27 from -60 to get -87.

$$34x-80=39x-87-18$$

Subtract 18 from -87 to get -105.

$$34x-80=39x-105$$

Subtract 39x from both sides.

$$34x-80-39x=-105$$

Combine 34x and -39x to get -5x.

$$-5x-80=-105$$

Add 80 to both sides.

$$-5x=-105+80$$

Add -105 and 80 to get -25.

$$-5x=-25$$

Divide both sides by -5.

$$x=\frac{-25}{-5}$$

Divide -25 by -5 to get 5.

$$x=5$$