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

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

Solve for x

$$x = \frac{27}{17} = 1\frac{10}{17} \approx 1.588235294$$

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 20x, the least common multiple of 5x,4,2x,5,4x.

$$4\times 3+20x\left(-\frac{1}{4}\right)-10\times 3=20x\times \frac{3}{5}-5\times 9$$

Do the multiplications.

$$12+20x\left(-\frac{1}{4}\right)-30=20x\times \frac{3}{5}-5\times 9$$

Multiply 20 and -\frac{1}{4} to get -5.

$$12-5x-30=20x\times \frac{3}{5}-5\times 9$$

Subtract 30 from 12 to get -18.

$$-18-5x=20x\times \frac{3}{5}-5\times 9$$

Multiply 20 and \frac{3}{5} to get 12.

$$-18-5x=12x-5\times 9$$

Multiply -5 and 9 to get -45.

$$-18-5x=12x-45$$

Subtract 12x from both sides.

$$-18-5x-12x=-45$$

Combine -5x and -12x to get -17x.

$$-18-17x=-45$$

Add 18 to both sides.

$$-17x=-45+18$$

Add -45 and 18 to get -27.

$$-17x=-27$$

Divide both sides by -17.

$$x=\frac{-27}{-17}$$

Fraction \frac{-27}{-17} can be simplified to \frac{27}{17} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{27}{17}$$