What is the answer to 1/((1-x)+\frac{x){10}}=5 ?

The answer to 1/((1-x)+\frac{x){10}}=5 is x= 8/9

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1/((1-x)+\frac{x){10}}=5

\frac{1}{( 1 - x ) + \frac{x}{10}} = 5

x = \frac{8}{9}

Decimal Notation

x = 0.88888 \dots

Solution steps

\frac{1}{( 1 - x ) + \frac{x}{10}} = 5

Simplify

\frac{1}{( 1 - x ) + \frac{x}{10}} : \frac{10}{10 - 9 x}

\frac{10}{10 - 9 x} = 5

Multiply both sides by

10 - 9 x

10 = 5 (10 - 9 x)

Switch sides

5 (10 - 9 x) = 10

Divide both sides by

5

10 - 9 x = 2

Move

10

to the right side

- 9 x = - 8

Divide both sides by

- 9

x = \frac{8}{9}

Verify Solutions

Find undefined (singularity) points:

x = \frac{10}{9}

Combine undefined points with solutions:

x = \frac{8}{9}

0.001 = \frac{x - 0.6032}{x}

\frac{8 y ^{2}}{2 y} = 40

\frac{16}{x + 7} = \frac{2}{6}

\frac{x}{x + 3} = \frac{6}{5}

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

What is the answer to 1/((1-x)+\frac{x){10}}=5 ?
The answer to 1/((1-x)+\frac{x){10}}=5 is x= 8/9
Solve for x: 1/((1-x)+\frac{x){10}}=5
The solution is x= 8/9