7 9/26-z=5 7/39

To solve the equation \( 7 \frac{9}{26} - z = 5 \frac{7}{39} \), we first need to convert the mixed numbers into improper fractions.

1. Convert the mixed numbers:

   For \( 7 \frac{9}{26} \): \[ 7 \frac{9}{26} = \frac{(7 \times 26) + 9}{26} = \frac{182 + 9}{26} = \frac{191}{26} \]

   For \( 5 \frac{7}{39} \): \[ 5 \frac{7}{39} = \frac{(5 \times 39) + 7}{39} = \frac{195 + 7}{39} = \frac{202}{39} \]

2. Substituting the improper fractions back into the equation: \[ \frac{191}{26} - z = \frac{202}{39} \]

3. Isolate \( z \): \[ -z = \frac{202}{39} - \frac{191}{26} \] \[ z = -\left(\frac{202}{39} - \frac{191}{26}\right) \]

4. Finding a common denominator to subtract the fractions:

   The least common multiple (LCM) of \( 39 \) and \( 26 \) is \( 78 \).

   Convert both fractions:

   For \( \frac{202}{39} \): \[ \frac{202}{39} \times \frac{2}{2} = \frac{404}{78} \]

   For \( \frac{191}{26} \): \[ \frac{191}{26} \times \frac{3}{3} = \frac{573}{78} \]

5. Now, substitute back into the equation: \[ z = -\left(\frac{404}{78} - \frac{573}{78}\right) \] \[ z = -\left(\frac{404 - 573}{78}\right) \] \[ z = -\left(\frac{-169}{78}\right) \] \[ z = \frac{169}{78} \]

Thus, the solution to the equation is: \[ z = \frac{169}{78} \]

If you require further simplification or conversion to a mixed number: \[ \frac{169}{78} = 2 \frac{13}{78} \]

Therefore: \[ z = 2 \frac{13}{78} \]