Solve 1/8+1/x=1/4.5

$$\frac { 1 } { 8 } + \frac { 1 } { x } = \frac { 1 } { 4.5 }$$

Solve for x

$$x = \frac{72}{7} = 10\frac{2}{7} \approx 10.285714286$$

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 8x, the least common multiple of 8,x.

$$8x\times \frac{1}{8}+8=8x\times \frac{1}{4.5}$$

Cancel out 8 and 8.

$$x+8=8x\times \frac{1}{4.5}$$

Expand \frac{1}{4.5} by multiplying both numerator and the denominator by 10.

$$x+8=8x\times \frac{10}{45}$$

Reduce the fraction \frac{10}{45} to lowest terms by extracting and canceling out 5.

$$x+8=8x\times \frac{2}{9}$$

Express 8\times \frac{2}{9} as a single fraction.

$$x+8=\frac{8\times 2}{9}x$$

Multiply 8 and 2 to get 16.

$$x+8=\frac{16}{9}x$$

Subtract \frac{16}{9}x from both sides.

$$x+8-\frac{16}{9}x=0$$

Combine x and -\frac{16}{9}x to get -\frac{7}{9}x.

$$-\frac{7}{9}x+8=0$$

Subtract 8 from both sides. Anything subtracted from zero gives its negation.

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

Multiply both sides by -\frac{9}{7}, the reciprocal of -\frac{7}{9}.

$$x=-8\left(-\frac{9}{7}\right)$$

Express -8\left(-\frac{9}{7}\right) as a single fraction.

$$x=\frac{-8\left(-9\right)}{7}$$

Multiply -8 and -9 to get 72.

$$x=\frac{72}{7}$$