
*CD* = *x* + 10

, 

*DE* = 5

, and 

*CE* = 4*x*

, what is *CE*?


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.

Explore how to solve equations involving segment lengths with variables such as CD = x + 10, DE = 5, and CE = 4x. This problem requires understanding linear equations and algebraic manipulation. Suitable for Grades 7-9.

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