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

To solve the equation \( x - 7 \frac{4}{5} = -4 \frac{2}{9} \), we will first convert the mixed numbers into improper fractions. 1. Convert \( 7 \frac{4}{5} \): \[ 7 \frac{4}{5} = 7 + \frac{4}{5} = \frac{7 \times 5 + 4}{5} = \frac{35 + 4}{5} = \frac{39}{5} \] 2. Convert \( -4 \frac{2}{9} \): \[ -4 \frac{2}{9} = -\left(4 + \frac{2}{9}\right) = -\left(\frac{4 \times 9 + 2}{9}\right) = -\left(\frac{36 + 2}{9}\right) = -\left(\frac{38}{9}\right) = -\frac{38}{9} \] Now we rewrite the equation using improper fractions: \[ x - \frac{39}{5} = -\frac{38}{9} \] Next, we'll isolate \( x \) by adding \( \frac{39}{5} \) to both sides: \[ x = -\frac{38}{9} + \frac{39}{5} \] To perform this addition, we need a common denominator. The least common multiple of 9 and 5 is 45. 3. Convert \( -\frac{38}{9} \) to have a denominator of 45: \[ -\frac{38}{9} = -\frac{38 \times 5}{9 \times 5} = -\frac{190}{45} \] 4. Convert \( \frac{39}{5} \) to have a denominator of 45: \[ \frac{39}{5} = \frac{39 \times 9}{5 \times 9} = \frac{351}{45} \] Now we can add the two fractions: \[ x = -\frac{190}{45} + \frac{351}{45} = \frac{351 - 190}{45} = \frac{161}{45} \] Thus, the solution for \( x \) is: \[ x = \frac{161}{45} \] If you want to convert this back to a mixed number: \[ 161 \div 45 = 3 \quad \text{(with a remainder of 26)} \] So, \[ \frac{161}{45} = 3 \frac{26}{45} \] The final answer is: \[ x = 3 \frac{26}{45} \]