\( ....-3\frac{4}{5}=7\frac{1}{3} \)

To solve the equation \( -3\frac{4}{5} = 7\frac{1}{3} \), we first need to convert the mixed numbers into improper fractions. 1. Convert \( -3\frac{4}{5} \): \[ -3\frac{4}{5} = -\left(3 \times 5 + 4\right)/5 = -\left(15 + 4\right)/5 = -\frac{19}{5} \] 2. Convert \( 7\frac{1}{3} \): \[ 7\frac{1}{3} = 7 \times 3 + 1/3 = \left(21 + 1\right)/3 = \frac{22}{3} \] Now we have the equation: \[ -\frac{19}{5} = \frac{22}{3} \] To solve for \( x \), we can set up the equation: \[ x - \frac{19}{5} = \frac{22}{3} \] Now, we can isolate \( x \): \[ x = \frac{22}{3} + \frac{19}{5} \] To add these fractions, we need a common denominator. The least common multiple of 3 and 5 is 15. Convert each fraction: \[ \frac{22}{3} = \frac{22 \times 5}{3 \times 5} = \frac{110}{15} \] \[ \frac{19}{5} = \frac{19 \times 3}{5 \times 3} = \frac{57}{15} \] Now we can add them: \[ x = \frac{110}{15} + \frac{57}{15} = \frac{110 + 57}{15} = \frac{167}{15} \] Thus, the solution to the equation is: \[ x = \frac{167}{15} \] If you want to convert this back to a mixed number: \[ \frac{167}{15} = 11\frac{2}{15} \] So, the final answer is: \[ x = 11\frac{2}{15} \]