What is the answer to 0.9=2-1/x ?

The answer to 0.9=2-1/x is x= 10/11

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0.9=2-1/x

0.9 = 2 - \frac{1}{x}

x = \frac{10}{11}

Decimal Notation

x = 0.90909 \dots

Solution steps

0.9 = 2 - \frac{1}{x}

Move

2

to the left side

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

Multiply both sides by

x

- 1.1 x = - 1

Multiply both sides by

10

- 11 x = - 10

Divide both sides by

- 11

x = \frac{10}{11}

Verify Solutions

Find undefined (singularity) points:

x = 0

Combine undefined points with solutions:

x = \frac{10}{11}

\frac{2}{x} = x - 43

\frac{( 2 x - 6 )}{( x - 3 )} = 14 - x

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

\frac{5}{9 x} = 1

8 - \frac{13}{x} = 4 + \frac{3}{x}