If UV = x − 4, VW = 5, and UW = 2x − 14, what is UV?

We are given three segments \( UV \), \( VW \), and \( UW \), and their algebraic expressions. We need to find the value of \( UV \).

### Step 1: Set up the equation
The relationship between the segments is:
\[
UV + VW = UW
\]
Substituting the given values:
\[
(x - 4) + 5 = 2x - 14
\]

### Step 2: Solve for \( x \)
Simplify the equation:
\[
x - 4 + 5 = 2x - 14
\]
\[
x + 1 = 2x - 14
\]
Subtract \( x \) from both sides:
\[
1 = x - 14
\]
Add 14 to both sides:
\[
x = 15
\]

### Step 3: Find \( UV \)
Now that we know \( x = 15 \), substitute it back into the expression for \( UV \):
\[
UV = x - 4 = 15 - 4 = 11
\]

Therefore, \( UV = 11 \).

Would you like more details or have any other questions?

Here are 5 related questions to explore:
1. What are the lengths of the other segments \( VW \) and \( UW \)?
2. How would the problem change if \( UW \) had a different expression?
3. Can you solve for \( x \) geometrically instead of algebraically?
4. What if \( UV \) were expressed as a quadratic equation?
5. How would solving this problem differ in a coordinate geometry context?

**Tip:** Always substitute your final solution back into the original equations to verify your answer.

Discover how to find the length of segment UV using algebraic equations in a geometric problem. Step-by-step solution provided for UV = x - 4, VW = 5, and UW = 2x - 14. Suitable for students in Grades 7-9.

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