Thanks for the images! Here's a breakdown of the mathematical problems.

Image 1:

1. First Problem: Given that D is the midpoint of AC, we have two expressions for the lengths of AD and DC:

   • $AD = 9x$
   • $DC = x + 4$

   Since D is the midpoint, $AD = DC$. So, we can set the two equations equal to each other: $9x = x + 4$ Solve for $x$ and then use that value to find $AC$, which is $AC = AD + DC$.

2. Second Problem: Here, D is also the midpoint, with:

   • $AD = 3x + 2$
   • $DC = 5x$

   Again, since D is the midpoint, $AD = DC$. Set the two expressions equal: $3x + 2 = 5x$ Solve for $x$, and then find $AC = AD + DC$.

Image 2:

The second image seems to be a geometry-related problem where you're tasked with completing statements about bisecting and finding midpoints.

1. First Task: The question is asking to bisect $AB$ at $E$, meaning $E$ is the midpoint of segment $AB$.

2. Second Task: The question asks to identify the point that is the midpoint of $AB$, which is what $E$ represents in the first task.

3. Third Task: The third task likely involves using the notation for congruent segments, indicated by the symbol $\cong$, to express that $AE \cong EB$.

Would you like me to work through the solutions to the problems step by step? Let me know if you need more clarification or help!

Here are 5 related questions you might explore:

1. What is the general formula for the midpoint of a segment?
2. How do you solve linear equations involving two variables?
3. What are the properties of congruent segments in geometry?
4. Can you apply the midpoint theorem to non-linear segments?
5. How would you calculate the perimeter of a triangle when given its side lengths?

Tip: Always check that your equations reflect the correct relationship (such as midpoint or congruency) before solving!