What is the answer to 1/(3x-1)=5 ?

The answer to 1/(3x-1)=5 is x= 2/5

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1/(3x-1)=5

\frac{1}{3 x - 1} = 5

x = \frac{2}{5}

Decimal Notation

x = 0.4

Solution steps

\frac{1}{3 x - 1} = 5

Multiply both sides by

3 x - 1

1 = 5 (3 x - 1)

Switch sides

5 (3 x - 1) = 1

Divide both sides by

5

3 x - 1 = \frac{1}{5}

Move

1

to the right side

3 x = \frac{6}{5}

Divide both sides by

3

x = \frac{2}{5}

Verify Solutions

Find undefined (singularity) points:

x = \frac{1}{3}

Combine undefined points with solutions:

x = \frac{2}{5}

\frac{1}{5} + \frac{1}{x} = \frac{1}{3.5}

\frac{2}{x ^{2} + 5 x + 6} = \frac{4}{x + 2}

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

y, x + \frac{1}{x} = y + \frac{1}{y}

\frac{x}{x + 9} + 1 = - \frac{1}{x + 9}