Solve 2/3x-5/x=3/10-3/2x

$$\frac{ 2 }{ 3x } - \frac{ 5 }{ x } = \frac{ 3 }{ 10 } - \frac{ 3 }{ 2x }$$

Solve for x

$$x = -\frac{85}{9} = -9\frac{4}{9} \approx -9.444444444$$

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 30x, the least common multiple of 3x,x,10,2x.

$$10\times 2-30\times 5=30x\times \frac{3}{10}-15\times 3$$

Do the multiplications.

$$20-150=30x\times \frac{3}{10}-15\times 3$$

Subtract 150 from 20 to get -130.

$$-130=30x\times \frac{3}{10}-15\times 3$$

Multiply 30 and \frac{3}{10} to get 9.

$$-130=9x-15\times 3$$

Multiply -15 and 3 to get -45.

$$-130=9x-45$$

Swap sides so that all variable terms are on the left hand side.

$$9x-45=-130$$

Add 45 to both sides.

$$9x=-130+45$$

Add -130 and 45 to get -85.

$$9x=-85$$

Divide both sides by 9.

$$x=\frac{-85}{9}$$

Fraction \frac{-85}{9} can be rewritten as -\frac{85}{9} by extracting the negative sign.

$$x=-\frac{85}{9}$$