What is the answer to 1+0.1=(1-x)^{-1} ?

The answer to 1+0.1=(1-x)^{-1} is x= 1/11

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1+0.1=(1-x)^{-1}

1 + 0.1 = (1 - x)^{- 1}

x = \frac{1}{11}

Decimal Notation

x = 0.09090 \dots

Solution steps

1 + 0.1 = (1 - x)^{- 1}

Refine

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

Multiply both sides by

1 - x

1.1 (1 - x) = 1

Multiply both sides by

10

11 (1 - x) = 10

Divide both sides by

11

1 - x = \frac{10}{11}

Move

1

to the right side

- x = - \frac{1}{11}

Divide both sides by

- 1

x = \frac{1}{11}

Verify Solutions

Find undefined (singularity) points:

x = 1

Combine undefined points with solutions:

x = \frac{1}{11}

\frac{2}{2 x + 1} - \frac{6}{x - 1} = 5

43 = 3 - \frac{5}{9 z}

\frac{4 - x}{x} = 0

33.6 x^{- 5} + 6.8 x^{- 4} - 501.37 = 0

\frac{0.5}{1} = \frac{10}{x}

What is the answer to 1+0.1=(1-x)^{-1} ?
The answer to 1+0.1=(1-x)^{-1} is x= 1/11
Solve for x: 1+0.1=(1-x)^{-1}
The solution is x= 1/11