What is the answer to 6= 1/(1-1/8 x) ?

The answer to 6= 1/(1-1/8 x) is x= 20/3

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6= 1/(1-1/8 x)

6 = \frac{1}{1 - \frac{1}{8} x}

x = \frac{20}{3}

Decimal Notation

x = 6.66666 \dots

Solution steps

6 = \frac{1}{1 - \frac{1}{8} x}

Simplify

\frac{1}{1 - \frac{1}{8} x} : \frac{8}{8 - x}

6 = \frac{8}{8 - x}

Multiply both sides by

8 - x

6 (8 - x) = 8

Divide both sides by

6

8 - x = \frac{4}{3}

Move

8

to the right side

- x = - \frac{20}{3}

Divide both sides by

- 1

x = \frac{20}{3}

Verify Solutions

Find undefined (singularity) points:

x = 8

Combine undefined points with solutions:

x = \frac{20}{3}

- 2 - \frac{6}{x} = \frac{- 7}{2}

\frac{2 p}{p - 1} = 3 + \frac{2}{p - 1}

\frac{x ^{2}}{( 2 - x ) ^{2}} = 0.0175

x, \frac{3}{x} + 2 y = - 3

\frac{6}{x} - x = 1