https://file.aiquickdraw.com/mathbot/file/17262561502917mhaczad.jpg

To find \( CE \), let's analyze the given information from the image:

### Line segment details:
- \( BC = 3x + 47 \)
- \( CD = 10 \)
- The total length of \( BE \) is composed of two parts:
  - \( BD = 27 + x \)
  - \( DE = x + 26 \)

We know that \( BE \) can be expressed in terms of these two segments:
\[
BE = BD + DE = (27 + x) + (x + 26)
\]
Simplifying this:
\[
BE = 27 + x + x + 26 = 2x + 53
\]

But we also know that \( BE \) is equal to the sum of \( BC \), \( CD \), and \( DE \). So:
\[
BE = BC + CD + DE = (3x + 47) + 10 + (x + 26)
\]
Simplifying the right-hand side:
\[
BE = 3x + 47 + 10 + x + 26 = 4x + 83
\]

Now, equate the two expressions for \( BE \):
\[
2x + 53 = 4x + 83
\]
Solve for \( x \):
\[
53 - 83 = 4x - 2x
\]
\[
-30 = 2x
\]
\[
x = -15
\]

### Finding \( CE \):
Now that we have \( x = -15 \), we can find \( CE \). We know that:
\[
CE = CD + DE = 10 + (x + 26)
\]
Substitute \( x = -15 \) into this expression:
\[
CE = 10 + (-15 + 26) = 10 + 11 = 21
\]

So, the length of \( CE \) is **21 units**.

Would you like more details or further explanations on any part of this solution?

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Here are 5 related questions you might want to explore:
1. How would the answer change if \( x \) had a different value?
2. Can you prove the calculation for \( BE \) using a different method?
3. What is the length of segment \( BC \) when \( x = -15 \)?
4. How would you calculate the total length of \( BE \)?
5. What geometric principles can you apply to similar problems?

**Tip**: When solving linear equations involving segments, breaking down the total distance into smaller known parts can make the calculations clearer.

Find the length of segment CE in the given line with BC = 3x + 47, CD = 10, BD = 27 + x, and DE = x + 26.

Learn how to solve for the length of segment CE in a line problem using algebra and the segment addition postulate. Given BC = 3x + 47, CD = 10, BD = 27 + x, and DE = x + 26, this step-by-step solution is perfect for Grades 8-10.

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