What is the answer to x/(0.1-x)=7.5 ?

The answer to x/(0.1-x)=7.5 is x=0.08823…

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x/(0.1-x)=7.5

\frac{x}{0.1 - x} = 7.5

x = 0.08823 \dots

Solution steps

\frac{x}{0.1 - x} = 7.5

Multiply both sides by

0.1 - x

x = 7.5 (0.1 - x)

Expand

7.5 (0.1 - x) : 0.75 - 7.5 x

x = 0.75 - 7.5 x

Move

7.5 x

to the left side

8.5 x = 0.75

Divide both sides by

8.5

x = 0.08823 \dots

Verify Solutions

Find undefined (singularity) points:

x = 0.1

Combine undefined points with solutions:

x = 0.08823 \dots

\frac{4}{x} = \frac{2}{5}

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

\frac{( x + 3 )}{x} = \frac{2}{5}

\frac{4}{x + 10} = \frac{4}{x - 3}

\frac{3}{x} + 2 = \frac{4}{5 x}