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.