To solve the equation \(3x + 2 = \frac{1}{9}\), follow these steps:

1. **Subtract 2 from both sides** to isolate the term involving \(x\):

   \[
   3x = \frac{1}{9} - 2
   \]

2. **Convert the 2 to a fraction** with a denominator of 9 to simplify the subtraction:

   \[
   2 = \frac{18}{9}
   \]
   
   So,

   \[
   3x = \frac{1}{9} - \frac{18}{9} = \frac{1 - 18}{9} = \frac{-17}{9}
   \]

3. **Divide both sides by 3** to solve for \(x\):

   \[
   x = \frac{-17}{9} \times \frac{1}{3} = \frac{-17}{27}
   \]

So, the solution is:

\[
x = \frac{-17}{27}
\]

Would you like more details or have any questions? Here are some related questions:

1. How do you convert improper fractions to mixed numbers?
2. What are the steps to solve linear equations involving fractions?
3. How do you check if a solution to an equation is correct?
4. What is the importance of isolating variables in algebra?
5. Can you explain how to handle negative numbers in fraction arithmetic?

**Tip:** When dealing with fractions in equations, it's often useful to work with a common denominator to simplify the process.

Learn how to solve the equation 3x + 2 = 1/9 with a detailed step-by-step solution. This problem covers key algebraic concepts, including linear equations and fractions. Suitable for students in Grades 7-9.

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