Solve 14/x=10.5/10-x

$$\frac { 14 } { x } = \frac { 10.5 } { 10 - x }$$

Solve for x

$$x = \frac{40}{7} = 5\frac{5}{7} \approx 5.714285714$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values 0,10 since division by zero is not defined. Multiply both sides of the equation by x\left(x-10\right), the least common multiple of x,10-x.

$$\left(x-10\right)\times 14=-x\times 10.5$$

Use the distributive property to multiply x-10 by 14.

$$14x-140=-x\times 10.5$$

Multiply -1 and 10.5 to get -10.5.

$$14x-140=-10.5x$$

Add 10.5x to both sides.

$$14x-140+10.5x=0$$

Combine 14x and 10.5x to get 24.5x.

$$24.5x-140=0$$

Add 140 to both sides. Anything plus zero gives itself.

$$24.5x=140$$

Divide both sides by 24.5.

$$x=\frac{140}{24.5}$$

Expand \frac{140}{24.5} by multiplying both numerator and the denominator by 10.

$$x=\frac{1400}{245}$$

Reduce the fraction \frac{1400}{245} to lowest terms by extracting and canceling out 35.

$$x=\frac{40}{7}$$