https://file.aiquickdraw.com/mathbot/file/17273589473637u0bttju.jpg

To solve this problem, let's break it down step-by-step:

We are given:
- AC = \( 10x + 6 \)
- AB = \( 5x \)
- BC = \( 4x + 12 \)

Since point B is between points A and C, the sum of AB and BC must be equal to AC:
\[
AB + BC = AC
\]

Substitute the given values:
\[
5x + (4x + 12) = 10x + 6
\]

Now, simplify and solve for \( x \):
\[
5x + 4x + 12 = 10x + 6
\]
\[
9x + 12 = 10x + 6
\]

Move all terms involving \( x \) to one side and constants to the other side:
\[
9x - 10x = 6 - 12
\]
\[
-x = -6
\]

Divide by -1:
\[
x = 6
\]

Thus, the value of \( x \) is 6.

### Answer: \( x = 6 \).

Would you like further details or have any questions about this solution? 

Here are 5 related questions for practice:
1. If AC = \( 15x + 2 \), AB = \( 3x \), and BC = \( 12x + 2 \), what is the value of \( x \)?
2. What happens to the equation if \( AB = 5x + 3 \) instead of \( 5x \)?
3. How do you solve for \( x \) if AC, AB, and BC were in terms of quadratic expressions?
4. Can you solve a similar problem if B is not exactly between A and C but some distance away?
5. How would this problem change if the segments were part of a geometric figure like a triangle?

### Tip: 
Always simplify both sides of the equation as much as possible before moving terms around to avoid mistakes.

Point B is between points A and C. AC=10x+6, AB=5x, and BC=4x+12. Find the value of x.

Solve the equation where point B is between points A and C with AC=10x+6, AB=5x, and BC=4x+12. Learn step-by-step how to find the value of x using algebraic methods and the Segment Addition Theorem. Suitable for Grades 8-10.

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