If 

*BC* = 3*x* − 16

, 

*CD* = *x* − 2

, and 

*BD* = 14

, what is *CD*?

We are given three segments \( BC \), \( CD \), and \( BD \), and their algebraic expressions. We need to find the value of \( CD \).

### Step 1: Set up the equation
The relationship between the segments is:
\[
BC + CD = BD
\]
Substituting the given values:
\[
(3x - 16) + (x - 2) = 14
\]

### Step 2: Solve for \( x \)
Simplify the equation:
\[
3x - 16 + x - 2 = 14
\]
Combine like terms:
\[
4x - 18 = 14
\]
Add 18 to both sides:
\[
4x = 32
\]
Divide both sides by 4:
\[
x = 8
\]

### Step 3: Find \( CD \)
Now that we know \( x = 8 \), substitute it back into the expression for \( CD \):
\[
CD = x - 2 = 8 - 2 = 6
\]

Therefore, \( CD = 6 \).

Would you like more details or have any other questions?

Here are 5 related questions to explore:
1. What is the value of \( BC \)?
2. How would the result change if the equation for \( BD \) were different?
3. What is the length of segment \( BC \) in this scenario?
4. How would this problem be approached if the segments were on a coordinate plane?
5. Can this problem be solved using a different algebraic method?

**Tip:** Always make sure to check your solution by substituting the value of \( x \) back into all the given segment equations.

Learn how to find the length of segment CD when given relationships with segments BC and BD. This problem involves solving a linear equation and is suitable for students in Grades 7-9.

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