(x-1/10)+4/15=7/9

To solve the equation \((x - \frac{1}{10}) + \frac{4}{15} = \frac{7}{9}\), we start by isolating \(x\).

1. First, combine like terms on the left side: \[ x - \frac{1}{10} + \frac{4}{15} = \frac{7}{9} \]

2. To combine \(-\frac{1}{10}\) and \(\frac{4}{15}\), we need a common denominator. The least common multiple of 10 and 15 is 30.

   Convert \(-\frac{1}{10}\) to a fraction with a denominator of 30: \[ -\frac{1}{10} = -\frac{3}{30} \]

   Convert \(\frac{4}{15}\) to a fraction with a denominator of 30: \[ \frac{4}{15} = \frac{8}{30} \]

   Now we can combine the two fractions: \[ -\frac{3}{30} + \frac{8}{30} = \frac{5}{30} = \frac{1}{6} \]

3. Substitute back into the equation: \[ x + \frac{1}{6} = \frac{7}{9} \]

4. To isolate \(x\), subtract \(\frac{1}{6}\) from both sides: \[ x = \frac{7}{9} - \frac{1}{6} \]

5. Now, we need a common denominator to subtract these fractions. The least common multiple of 9 and 6 is 18.

   Convert \(\frac{7}{9}\) to a fraction with a denominator of 18: \[ \frac{7}{9} = \frac{14}{18} \]

   Convert \(\frac{1}{6}\) to a fraction with a denominator of 18: \[ \frac{1}{6} = \frac{3}{18} \]

6. Now, perform the subtraction: \[ x = \frac{14}{18} - \frac{3}{18} = \frac{11}{18} \]

Thus, the solution is: \[ \boxed{\frac{11}{18}} \]