Solve 4x/15-5x/6+6=7x/18-5x/12-frac{5}{9}+frac{139}{36}

$$\frac { 4 x } { 15 } - \frac { 5 x } { 6 } + 6 = \frac { 7 x } { 18 } - \frac { 5 x } { 12 } - \frac { 5 } { 9 } + \frac { 139 } { 36 }$$

Solve for x

$$x=5$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 180, the least common multiple of 15,6,18,12,9,36.

$$12\times 4x-30\times 5x+1080=10\times 7x-15\times 5x-100+695$$

Multiply 12 and 4 to get 48.

$$48x-30\times 5x+1080=10\times 7x-15\times 5x-100+695$$

Multiply -30 and 5 to get -150.

$$48x-150x+1080=10\times 7x-15\times 5x-100+695$$

Combine 48x and -150x to get -102x.

$$-102x+1080=10\times 7x-15\times 5x-100+695$$

Multiply 10 and 7 to get 70. Multiply -15 and 5 to get -75.

$$-102x+1080=70x-75x-100+695$$

Combine 70x and -75x to get -5x.

$$-102x+1080=-5x-100+695$$

Add -100 and 695 to get 595.

$$-102x+1080=-5x+595$$

Add 5x to both sides.

$$-102x+1080+5x=595$$

Combine -102x and 5x to get -97x.

$$-97x+1080=595$$

Subtract 1080 from both sides.

$$-97x=595-1080$$

Subtract 1080 from 595 to get -485.

$$-97x=-485$$

Divide both sides by -97.

$$x=\frac{-485}{-97}$$

Divide -485 by -97 to get 5.

$$x=5$$