What is the answer to 1= 2/3-(x-7)/x ?

The answer to 1= 2/3-(x-7)/x is x= 21/4

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1= 2/3-(x-7)/x

1 = \frac{2}{3} - \frac{x - 7}{x}

x = \frac{21}{4}

Decimal Notation

x = 5.25

Solution steps

1 = \frac{2}{3} - \frac{x - 7}{x}

Multiply by LCM

3 x = 2 x - 3 (x - 7)

Expand

- 3 (x - 7) : - 3 x + 21

3 x = 2 x - 3 x + 21

Add similar elements:

2 x - 3 x = - x

3 x = - x + 21

Move

x

to the left side

4 x = 21

Divide both sides by

4

x = \frac{21}{4}

Verify Solutions

Find undefined (singularity) points:

x = 0

Combine undefined points with solutions:

x = \frac{21}{4}

\frac{2 x - 1}{4 - 3 x} = \frac{3}{4}

x = \frac{- 20 x}{12 - 150 x}

1 - \frac{64}{x ^{3}} = 0

\frac{84}{49} = \frac{576}{x}

\frac{2}{3} = \frac{6}{q - 4}