What is the answer to 9x-2-7x(1/x-1/2)=((1+x/2))/2+23/4 ?

The answer to 9x-2-7x(1/x-1/2)=((1+x/2))/2+23/4 is x= 61/49

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9x-2-7x(1/x-1/2)=((1+x/2))/2+23/4

9 x - 2 - 7 x (\frac{1}{x} - \frac{1}{2}) = \frac{( 1 + \frac{x}{2} )}{2} + \frac{23}{4}

x = \frac{61}{49}

Decimal Notation

x = 1.24489 \dots

Solution steps

9 x - 2 - 7 x (\frac{1}{x} - \frac{1}{2}) = \frac{( 1 + \frac{x}{2} )}{2} + \frac{23}{4}

Multiply by LCM

50 x - 36 = x + 25

Move

36

to the right side

50 x = x + 61

Move

x

to the left side

49 x = 61

Divide both sides by

49

x = \frac{61}{49}

Verify Solutions

Find undefined (singularity) points:

x = 0

Combine undefined points with solutions:

x = \frac{61}{49}

x, \frac{1}{x} = \frac{4}{( y - x ) ^{2}}

\frac{6 q ^{2} + 1}{2} = \frac{7}{2 q}

\frac{\frac{16}{7}}{\frac{4}{9}} = \frac{\frac{9}{14}}{t}

(\frac{x}{( x + 5 )}) - (\frac{11 x}{( 11 x - 8 )}) + (\frac{7}{( 6 - 4 x )}) = 0

x^{- 4} - 6 x^{- 2} + 8 = 0

What is the answer to 9x-2-7x(1/x-1/2)=((1+x/2))/2+23/4 ?
The answer to 9x-2-7x(1/x-1/2)=((1+x/2))/2+23/4 is x= 61/49
Solve for x: 9x-2-7x(1/x-1/2)=((1+x/2))/2+23/4
The solution is x= 61/49