Question

if uv = x - 2, vw = 3x - 13, and uw = 9, what is vw?
diagram: u---v---w with uv labeled x-2, vw labeled 3x-13, uw labeled 9
simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Set up the equation

From the segment addition postulate, we know that \( UV + VW = UW \). Substituting the given expressions, we get \((x - 2)+(3x - 13)=9\).

Step2: Simplify the left side

Combine like terms: \( x - 2 + 3x - 13 = 4x - 15 \). So the equation becomes \( 4x - 15 = 9 \).

Step3: Solve for x

Add 15 to both sides: \( 4x = 9 + 15 \), which simplifies to \( 4x = 24 \). Then divide both sides by 4: \( x=\frac{24}{4}=6 \).

Step4: Find VW

Substitute \( x = 6 \) into the expression for \( VW \), which is \( 3x - 13 \). So \( VW = 3(6)-13 = 18 - 13 = 5 \).

Answer:

\( 5 \)