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