x - 7 4/5=-4 2/9

To solve the equation \( x - 7 \frac{4}{5} = -4 \frac{2}{9} \), we first convert the mixed numbers into improper fractions.

1. Convert \( 7 \frac{4}{5} \): \[ 7 \frac{4}{5} = 7 \times 5 + 4 = 35 + 4 = 39 \frac{4}{5} = \frac{39 \times 5 + 4}{5} = \frac{39 + 4}{5} = \frac{199}{5} \]

2. Convert \( -4 \frac{2}{9} \): \[ -4 \frac{2}{9} = -\left(4 \times 9 + 2\right) = -\left(36 + 2\right) = -38 \]

So now we have:

\[ x - \frac{39}{5} = -\frac{38}{9} \]

Next, we need to add \( \frac{39}{5} \) to both sides to isolate \( x \):

\[ x = -\frac{38}{9} + \frac{39}{5} \]

To perform this addition, we need a common denominator, which is \( 45 \).

1. Convert \( -\frac{38}{9} \) to the common denominator: \[ -\frac{38}{9} = -\frac{38 \times 5}{45} = -\frac{190}{45} \]

2. Convert \( \frac{39}{5} \) to the common denominator: \[ \frac{39}{5} = \frac{39 \times 9}{45} = \frac{351}{45} \]

Now we can add the fractions:

\[ x = -\frac{190}{45} + \frac{351}{45} = \frac{351 - 190}{45} = \frac{161}{45} \]

Thus, the solution is:

\[ x = \frac{161}{45} \]

You can also convert this back to a mixed number, if desired:

\[ \frac{161}{45} = 3 \frac{26}{45} \]

So, the final answer is: \[ x = \frac{161}{45} \quad \text{or} \quad x = 3 \frac{26}{45} \]