What is the answer to 1/8+1/x = 1/2 ?

The answer to 1/8+1/x = 1/2 is x= 8/3

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1/8+1/x = 1/2

\frac{1}{8} + \frac{1}{x} = \frac{1}{2}

x = \frac{8}{3}

Decimal Notation

x = 2.66666 \dots

Solution steps

\frac{1}{8} + \frac{1}{x} = \frac{1}{2}

Multiply by LCM

x + 8 = 4 x

Move

8

to the right side

x = 4 x - 8

Move

4 x

to the left side

- 3 x = - 8

Divide both sides by

- 3

x = \frac{8}{3}

Verify Solutions

Find undefined (singularity) points:

x = 0

Combine undefined points with solutions:

x = \frac{8}{3}

2 x + \frac{16}{x ^{2}} = 0

0 = 1 - \frac{9}{x ^{2}}

3 - \frac{2}{x + 4} = - \frac{2 x}{x + 4}

\frac{3}{2} + \frac{1}{3} = \frac{1}{x}

\frac{4}{x ^{2}} + \frac{4}{x} = 3