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The image shows a math problem related to geometry, specifically dealing with triangles. The question asks for the value of \( x \), given the following equation:

\[
\text{If} \, 3x + 10 = 9x + 8, \, \text{what is the value of} \, x?
\]

### Solving the Equation:
To solve for \( x \), follow these steps:

1. **Subtract \( 3x \) from both sides:**

   \[
   3x + 10 - 3x = 9x + 8 - 3x
   \]

   Simplifying this, we get:

   \[
   10 = 6x + 8
   \]

2. **Subtract 8 from both sides:**

   \[
   10 - 8 = 6x + 8 - 8
   \]

   Simplifying this, we get:

   \[
   2 = 6x
   \]

3. **Divide both sides by 6:**

   \[
   \frac{2}{6} = x
   \]

   Simplifying this, we get:

   \[
   x = \frac{1}{3}
   \]

### Answer:
The value of \( x \) is \( \frac{1}{3} \).

Would you like further details on this solution, or do you have any other questions?

### Related Questions:
1. What is the process for solving linear equations involving variables on both sides?
2. How do you handle equations that involve fractions or decimals?
3. Can the value of \( x \) be negative in linear equations? Under what conditions?
4. How do you check if your solution to a linear equation is correct?
5. How can you solve linear equations with more than one variable?

### Tip:
Always check your solution by substituting the value of \( x \) back into the original equation to ensure it satisfies the equation.

If 3x + 10 = 9x + 8, what is the value of x?

Learn how to solve the linear equation 3x + 10 = 9x + 8 with a detailed step-by-step solution. This problem covers key algebraic concepts, including manipulating linear equations and applying the properties of equality. Suitable for students in Grades 6-8.

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