Solve 2/x+4=7/3x+37/9

$$\frac { 2 } { x } + 4 = \frac { 7 } { 3 x } + \frac { 37 } { 9 }$$

Solve for x

$$x=-3$$

Steps for Solving Linear Equation

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 9x, the least common multiple of x,3x,9.

$$9\times 2+9x\times 4=3\times 7+9x\times \frac{37}{9}$$

Multiply 9 and 2 to get 18.

$$18+9x\times 4=3\times 7+9x\times \frac{37}{9}$$

Multiply 9 and 4 to get 36.

$$18+36x=3\times 7+9x\times \frac{37}{9}$$

Multiply 3 and 7 to get 21.

$$18+36x=21+9x\times \frac{37}{9}$$

Multiply 9 and \frac{37}{9} to get 37.

$$18+36x=21+37x$$

Subtract 37x from both sides.

$$18+36x-37x=21$$

Combine 36x and -37x to get -x.

$$18-x=21$$

Subtract 18 from both sides.

$$-x=21-18$$

Subtract 18 from 21 to get 3.

$$-x=3$$

Multiply both sides by -1.

$$x=-3$$