What is the answer to 1/(2x-1)=3x+1 ?

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

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1/(2x-1)=3x+1

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

x = \frac{2}{3}, x = - \frac{1}{2}

Decimal Notation

x = 0.66666 \dots, x = - 0.5

Solution steps

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

Multiply both sides by

2 x - 1

1 = 3 x (2 x - 1) + 2 x - 1

Solve

1 = 3 x (2 x - 1) + 2 x - 1 : x = \frac{2}{3}, x = - \frac{1}{2}

x = \frac{2}{3}, x = - \frac{1}{2}

Verify Solutions

Find undefined (singularity) points:

x = \frac{1}{2}

Combine undefined points with solutions:

x = \frac{2}{3}, x = - \frac{1}{2}

f, f^{- 1} (x) = \frac{- 2 x + 2}{x + 7}

\frac{x - 7}{2 x - 9} = \frac{4}{3}

\frac{1}{x} + 2 = - \frac{5}{x ^{2} + 6 x}

\frac{2}{( x + 1 ) ^{3}} = 0

\frac{4 x - 1}{2 x + 3} = \frac{2 x + 1}{6 x + 5}

What is the answer to 1/(2x-1)=3x+1 ?
The answer to 1/(2x-1)=3x+1 is x= 2/3 ,x=-1/2
Solve for x: 1/(2x-1)=3x+1
The solution is x= 2/3 ,x=-1/2