What is the answer to (2x)/(x-5)= 2/3 ?

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

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(2x)/(x-5)= 2/3

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

x = - \frac{5}{2}

Decimal Notation

x = - 2.5

Solution steps

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

Cross multiply

6 x = 2 x - 10

Move

2 x

to the left side

4 x = - 10

Divide both sides by

4

x = - \frac{5}{2}

Verify Solutions

Find undefined (singularity) points:

x = 5

Combine undefined points with solutions:

x = - \frac{5}{2}

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

x + \frac{6}{x} = 4

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

\frac{7}{x} + \frac{3}{2} = 2

\frac{3 x + 2}{4} = 5 - \frac{9 x + 14}{12 x}