Solve 1/8.5=1/150+1/x

$$\frac{ 1 }{ 8.5 } = \frac{ 1 }{ 150 } + \frac{ 1 }{ x }$$

Solve for x

$$x = \frac{2550}{283} = 9\frac{3}{283} \approx 9.010600707$$

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 150x, the least common multiple of 150,x.

$$150x\times \frac{1}{8.5}=150x\times \frac{1}{150}+150$$

Expand \frac{1}{8.5} by multiplying both numerator and the denominator by 10.

$$150x\times \frac{10}{85}=150x\times \frac{1}{150}+150$$

Reduce the fraction \frac{10}{85} to lowest terms by extracting and canceling out 5.

$$150x\times \frac{2}{17}=150x\times \frac{1}{150}+150$$

Express 150\times \frac{2}{17} as a single fraction.

$$\frac{150\times 2}{17}x=150x\times \frac{1}{150}+150$$

Multiply 150 and 2 to get 300.

$$\frac{300}{17}x=150x\times \frac{1}{150}+150$$

Cancel out 150 and 150.

$$\frac{300}{17}x=x+150$$

Subtract x from both sides.

$$\frac{300}{17}x-x=150$$

Combine \frac{300}{17}x and -x to get \frac{283}{17}x.

$$\frac{283}{17}x=150$$

Multiply both sides by \frac{17}{283}, the reciprocal of \frac{283}{17}.

$$x=150\times \frac{17}{283}$$

Express 150\times \frac{17}{283} as a single fraction.

$$x=\frac{150\times 17}{283}$$

Multiply 150 and 17 to get 2550.

$$x=\frac{2550}{283}$$