Solve 10/x-7/5=8/x-9/10

$$\frac { 10 } { x } - \frac { 7 } { 5 } = \frac { 8 } { x } - \frac { 9 } { 10 }$$

Solve for x

$$x=4$$

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 x,5,10.

$$10\times 10+10x\left(-\frac{7}{5}\right)=10\times 8+10x\left(-\frac{9}{10}\right)$$

Multiply 10 and 10 to get 100.

$$100+10x\left(-\frac{7}{5}\right)=10\times 8+10x\left(-\frac{9}{10}\right)$$

Express 10\left(-\frac{7}{5}\right) as a single fraction.

$$100+\frac{10\left(-7\right)}{5}x=10\times 8+10x\left(-\frac{9}{10}\right)$$

Multiply 10 and -7 to get -70.

$$100+\frac{-70}{5}x=10\times 8+10x\left(-\frac{9}{10}\right)$$

Divide -70 by 5 to get -14.

$$100-14x=10\times 8+10x\left(-\frac{9}{10}\right)$$

Multiply 10 and 8 to get 80.

$$100-14x=80+10x\left(-\frac{9}{10}\right)$$

Cancel out 10 and 10.

$$100-14x=80-9x$$

Add 9x to both sides.

$$100-14x+9x=80$$

Combine -14x and 9x to get -5x.

$$100-5x=80$$

Subtract 100 from both sides.

$$-5x=80-100$$

Subtract 100 from 80 to get -20.

$$-5x=-20$$

Divide both sides by -5.

$$x=\frac{-20}{-5}$$

Divide -20 by -5 to get 4.

$$x=4$$