What is the answer to 78(1-1/x)=116 ?

The answer to 78(1-1/x)=116 is x=-39/19

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78(1-1/x)=116

78 (1 - \frac{1}{x}) = 116

x = - \frac{39}{19}

Decimal Notation

x = - 2.05263 \dots

Solution steps

78 (1 - \frac{1}{x}) = 116

Expand

78 (1 - \frac{1}{x}) : 78 - \frac{78}{x}

78 - \frac{78}{x} = 116

Move

78

to the right side

- \frac{78}{x} = 38

Multiply both sides by

x

- 78 = 38 x

Switch sides

38 x = - 78

Divide both sides by

38

x = - \frac{39}{19}

Verify Solutions

Find undefined (singularity) points:

x = 0

Combine undefined points with solutions:

x = - \frac{39}{19}

\frac{20}{x} = \frac{30}{x - 2}

1 0^{3} = \frac{I}{I}

\frac{400}{x} = 80

(x - 3)^{- 2} = 25

0 = \frac{x + 1}{x ^{2} - 81}