Given the following equations: $CD = x + 10$ $DE = 5$ $CE = 4x$ and knowing that $CE$ is the total length of $CD$ plus $DE$, we can write: $CE = CD + DE$

Substituting the given values: $4x = (x + 10) + 5$

Simplify the equation: $4x = x + 15$

Now, solve for $x$: $4x - x = 15$ $3x = 15$ $x = 5$

Finally, substitute $x = 5$ back into the equation for $CE$: $CE = 4x = 4(5) = 20$

Thus, the length of $CE$ is $\boxed{20}$.

Would you like more details or have any questions?

Here are 8 related questions for further practice:

1. If $CD = 2x + 3$, $DE = 7$, and $CE = 6x$, what is $CE$?
2. If $CD = x + 4$, $DE = 2x$, and $CE = 3x + 4$, what is the value of $x$?
3. If $CD = x + 8$, $DE = 12$, and $CE = 5x$, solve for $CE$.
4. If $CD = 2x - 1$, $DE = 3x + 1$, and $CE = 7x$, what is the value of $x$ and $CE$?
5. How would the problem change if $CD = x + 5$, $DE = 4$, and $CE = 3x + 2$?
6. If $CD = 3x + 9$, $DE = 2x$, and $CE = 7x + 2$, find the value of $CE$.
7. How would the situation change if $CE$ was not simply $CD + DE$ but a different relationship?
8. What is the value of $x$ if $CE = 12$, $CD = 3x$, and $DE = 5x - 6$?

Tip: When combining lengths of segments to form a larger segment, always check that the sum of the parts equals the total length given.