https://file.aiquickdraw.com/mathbot/file/17289093523511mvb19o4.jpg

In the image, the problem provides the following information about a straight line:

- \( AB = 2x + 3 \)
- \( BC = 3x - 5 \)
- \( AC = 38 \)

Since \( A \), \( B \), and \( C \) are on the same straight line, the sum of segments \( AB \) and \( BC \) must equal \( AC \). Therefore, we can set up the following equation:

\[
AB + BC = AC
\]

Substitute the given values:

\[
(2x + 3) + (3x - 5) = 38
\]

Simplify the equation:

\[
2x + 3x + 3 - 5 = 38
\]
\[
5x - 2 = 38
\]

Now, solve for \( x \):

\[
5x = 38 + 2
\]
\[
5x = 40
\]
\[
x = \frac{40}{5} = 8
\]

Thus, the value of \( x \) is \( \boxed{8} \).

Do you need any further details or have additional questions?

Here are 5 related questions to expand on this:
1. What would happen if the value of \( AC \) changed to 45?
2. Can you express \( BC \) in terms of \( AB \) for a general case?
3. How would the problem change if the points weren't collinear?
4. What if one of the expressions for \( AB \) or \( BC \) included a quadratic term?
5. How would this concept apply to three-dimensional geometry?

**Tip:** Always check whether given points are collinear in problems involving straight lines, as this helps simplify calculations by applying straightforward addition.

If AB = 2x + 3, BC = 3x - 5, and AC = 38, what is the value of x?

Learn how to solve a linear equation where AB = 2x + 3, BC = 3x - 5, and AC = 38, using basic algebra. This problem explores key concepts such as linear equations, addition of segments, and collinear points, suitable for Grades 6-8.

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