We are given the following information from the problem:

• $AB = 2x + 10$
• $BC = x$
• $AC = 5x$

Since $B$ is a point on the line segment $AC$, the sum of the segments $AB$ and $BC$ must be equal to $AC$. Therefore, we can set up the equation:

$AB + BC = AC$

Substitute the given values into the equation:

$(2x + 10) + x = 5x$

Now, solve for $x$:

$2x + x + 10 = 5x$ $3x + 10 = 5x$ $10 = 5x - 3x$ $10 = 2x$ $x = 5$

Now that we know $x = 5$, we can determine the length of $AC$ by substituting $x$ back into the expression for $AC$:

$AC = 5x = 5(5) = 25$

Therefore, the numerical length of $AC$ is $25$.

Let me know if you need more details or have any questions!

Here are some related questions you might explore:

1. What is the value of segment $AB$?
2. How do you calculate the length of segment $BC$?
3. If $AB + BC = AC$, what happens if $B$ is not between $A$ and $C$?
4. Can you solve for $x$ if a different equation for $AC$ was given, like $AC = 4x$?
5. How do you verify the solution by plugging back into the original equation?

Tip: Always recheck your solution by substituting values back into the original equation to avoid mistakes!