What is the answer to ((x+4)/(2x-1))=2 ?

The answer to ((x+4)/(2x-1))=2 is x=2

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((x+4)/(2x-1))=2

(\frac{x + 4}{2 x - 1}) = 2

x = 2

Solution steps

(\frac{x + 4}{2 x - 1}) = 2

Simplify

(\frac{x + 4}{2 x - 1}) : \frac{x + 4}{2 x - 1}

\frac{x + 4}{2 x - 1} = 2

Multiply both sides by

2 x - 1

x + 4 = 2 (2 x - 1)

Expand

2 (2 x - 1) : 4 x - 2

x + 4 = 4 x - 2

Move

4

to the right side

x = 4 x - 6

Move

4 x

to the left side

- 3 x = - 6

Divide both sides by

- 3

x = 2

Verify Solutions

Find undefined (singularity) points:

x = \frac{1}{2}

Combine undefined points with solutions:

x = 2

6 - \frac{3}{x} = \frac{9}{2}

u, y = \frac{u + 1}{u + 2}

5 x^{- 2} - 14 x^{- 1} - 3 = 0

\frac{40}{x - 4} + 7 = \frac{3}{x - 4}

4 x + \frac{4}{x} + 11 = 0