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.