Question

if uv = 13x, vw = 9x − 15, and uw = 20x + 19, what is uv?
diagram: u---v---w with uv labeled 13x, vw labeled 9x−15, uw labeled 20x+19
simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Apply segment addition postulate

From the diagram, \( UV + VW = UW \). Substitute the given expressions: \( 13x + (9x - 15) = 20x + 19 \).

Step2: Simplify left side

Combine like terms: \( 13x + 9x - 15 = 22x - 15 \). So the equation is \( 22x - 15 = 20x + 19 \).

Step3: Solve for \( x \)

Subtract \( 20x \) from both sides: \( 22x - 20x - 15 = 19 \), which simplifies to \( 2x - 15 = 19 \). Then add 15 to both sides: \( 2x = 19 + 15 = 34 \). Divide by 2: \( x = \frac{34}{2} = 17 \).

Step4: Find \( UV \)

Since \( UV = 13x \), substitute \( x = 17 \): \( UV = 13 \times 17 = 221 \).

Answer:

221