(х-5/6)+11/18=19/24

To solve the equation \((x - \frac{5}{6}) + \frac{11}{18} = \frac{19}{24}\), follow these steps: 1. **Isolate \(x\)**: \[ x - \frac{5}{6} = \frac{19}{24} - \frac{11}{18} \] 2. **Find a common denominator** for \(\frac{19}{24}\) and \(\frac{11}{18}\). The least common multiple of 24 and 18 is 72. 3. **Convert both fractions**: \[ \frac{19}{24} = \frac{19 \times 3}{24 \times 3} = \frac{57}{72} \] \[ \frac{11}{18} = \frac{11 \times 4}{18 \times 4} = \frac{44}{72} \] 4. **Subtract the fractions**: \[ \frac{19}{24} - \frac{11}{18} = \frac{57}{72} - \frac{44}{72} = \frac{13}{72} \] 5. **Substituting back**: \[ x - \frac{5}{6} = \frac{13}{72} \] 6. **Add \(\frac{5}{6}\) to both sides**. First, convert \(\frac{5}{6}\) to have a common denominator of 72: \[ \frac{5}{6} = \frac{5 \times 12}{6 \times 12} = \frac{60}{72} \] Now add: \[ x = \frac{13}{72} + \frac{60}{72} = \frac{73}{72} \] 7. **Conclusion**: The solution to the equation is \[ x = \frac{73}{72} \]