https://file.aiquickdraw.com/mathbot/file/1725467132555ntat26kk.jpg

In the image provided, the two expressions \(3x + 8\) and \(6x + 10\) are placed on angles that appear to be vertically opposite angles. Since vertically opposite angles are always equal, we can set the expressions equal to each other and solve for \(x\):

\[
3x + 8 = 6x + 10
\]

Now, let's solve this equation:

1. Subtract \(3x\) from both sides:
\[
8 = 3x + 10
\]

2. Subtract 10 from both sides:
\[
8 - 10 = 3x
\]

3. Simplify:
\[
-2 = 3x
\]

4. Divide by 3:
\[
x = -\frac{2}{3}
\]

So, the solution is \(x = -\frac{2}{3}\).

Would you like a detailed explanation, or do you have any further questions on this? 

Here are five related questions you might find helpful:

1. What are vertically opposite angles, and why are they equal?
2. How do you solve equations with variables on both sides?
3. Can vertically opposite angles be supplementary?
4. How can you verify the solution to an equation like the one above?
5. What happens if \(x\) in the equation represents a real-world quantity, like time or distance?

**Tip:** When solving equations, always try to isolate the variable on one side by performing inverse operations.

Learn how to solve for x by using the properties of vertically opposite angles. This problem involves setting up and solving a linear equation, suitable for students in Grades 7-10.

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