X+x/9=-10/3

To solve the equation \( x + \frac{x}{9} = -\frac{10}{3} \), follow these steps:

1. Combine the terms on the left side: First, we can get a common denominator for the terms that contain \( x \). The term \( x \) can be rewritten with a denominator of 9:

   \[ x = \frac{9x}{9} \]

   Now we can combine:

   \[ \frac{9x}{9} + \frac{x}{9} = -\frac{10}{3} \]

   This simplifies to:

   \[ \frac{10x}{9} = -\frac{10}{3} \]

2. Clear the fraction by cross-multiplying: Multiply both sides by 9 to eliminate the denominator:

   \[ 10x = -\frac{10}{3} \times 9 \]

   Simplifying the right side gives:

   \[ 10x = -30 \]

3. Solve for \( x \): Divide both sides by 10:

   \[ x = -3 \]

Thus, the solution to the equation \( x + \frac{x}{9} = -\frac{10}{3} \) is:

\[ \boxed{-3} \]