Let's break down the problem systematically:

Given Information:

• B is between A and C.
• C is between B and D.
• $AB = 6$, $CD = 4$, and $BC = 13$.

We are tasked with evaluating the expression $(AD - CD) + AC$.

Step-by-Step Solution:

1. Find AC: Since $B$ is between $A$ and $C$, we have: $AC = AB + BC = 6 + 13 = 19.$

2. Find AD: Since $C$ is between $B$ and $D$, we have: $AD = AC + CD = 19 + 4 = 23.$

3. Evaluate $AD - CD$: $AD - CD = 23 - 4 = 19.$

4. Final Expression: Now, we evaluate the entire expression: $(AD - CD) + AC = 19 + 19 = 38.$

Thus, the value of the expression $(AD - CD) + AC$ is $\boxed{38}$.

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Do you need more details on any step or have any questions?

Here are 5 related questions you can explore:

1. What is the significance of point positioning in geometry problems?
2. How do segment addition and subtraction work in a number line context?
3. Can you apply this method to solve problems with unknown segment lengths?
4. What if the lengths were variables? How would the solution process change?
5. How do relative positions of points affect distance calculations in geometry?

Tip: Always draw a diagram when working with geometric positions to visualize relationships between points clearly!