Thanks for the clarification! Given that the distance between points \(A\) and \(B\) is \(3x - 2\) instead of \(3x + 2\), let's solve the problem again.

The distances are:
- \(AB = 3x - 2\)
- \(BC = 4x + 5\)
- Total distance \(AC = 17\)

We can set up the equation by adding the distances between \(A\) and \(B\) and between \(B\) and \(C\) to equal the total distance \(AC\):

\[
(3x - 2) + (4x + 5) = 17
\]

Now, combine like terms:

\[
7x + 3 = 17
\]

Next, subtract 3 from both sides:

\[
7x = 14
\]

Finally, divide by 7:

\[
x = 2
\]

So, \(x = 2\).

Would you like any further details or have any questions? 

Here are some follow-up questions you might find helpful:
1. What is the length of segment \(AB\) when \(x = 2\)?
2. What is the length of segment \(BC\) when \(x = 2\)?
3. How can we verify that the sum of segments \(AB\) and \(BC\) equals 17?
4. If \(x\) were to change, how would it affect the lengths of \(AB\) and \(BC\)?
5. Can you solve a similar problem where \(AC\) is a different value?

**Tip:** Always double-check the problem details before solving, especially when dealing with algebraic expressions!

Learn how to solve a distance problem involving algebraic expressions like 3x - 2 and 3x + 2. Detailed step-by-step solution provided, addressing the correct interpretation of expressions in the problem. Suitable for high school students studying algebra.

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