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.