Solve 3/2x-7/5=4/5x-5/2

$$\frac { 3 } { 2 x } - \frac { 7 } { 5 } = \frac { 4 } { 5 x } - \frac { 5 } { 2 }$$

Solve for x

$$x=-\frac{7}{11}\approx -0.636363636$$

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 10x, the least common multiple of 2x,5,5x,2.

$$5\times 3+10x\left(-\frac{7}{5}\right)=2\times 4+10x\left(-\frac{5}{2}\right)$$

Multiply 5 and 3 to get 15.

$$15+10x\left(-\frac{7}{5}\right)=2\times 4+10x\left(-\frac{5}{2}\right)$$

Multiply 10 and -\frac{7}{5} to get -14.

$$15-14x=2\times 4+10x\left(-\frac{5}{2}\right)$$

Multiply 2 and 4 to get 8.

$$15-14x=8+10x\left(-\frac{5}{2}\right)$$

Multiply 10 and -\frac{5}{2} to get -25.

$$15-14x=8-25x$$

Add 25x to both sides.

$$15-14x+25x=8$$

Combine -14x and 25x to get 11x.

$$15+11x=8$$

Subtract 15 from both sides.

$$11x=8-15$$

Subtract 15 from 8 to get -7.

$$11x=-7$$

Divide both sides by 11.

$$x=\frac{-7}{11}$$

Fraction \frac{-7}{11} can be rewritten as -\frac{7}{11} by extracting the negative sign.

$$x=-\frac{7}{11}$$