Question

if uv = 12, vw = x - 6, and uw = 2x - 6, what is uw?
u ---- v ---- w (with uv labeled 12, vw labeled x - 6, uw labeled 2x - 6)
simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Apply segment addition postulate

From the number line, we know that \( UV + VW = UW \). Substituting the given values, we get \( 12+(x - 6)=2x - 6 \).

Step2: Simplify the left - hand side

Simplify \( 12+(x - 6) \): \( 12+x - 6=x + 6 \). So the equation becomes \( x + 6=2x - 6 \).

Step3: Solve for x

Subtract \( x \) from both sides: \( x+6 - x=2x - 6 - x \), which simplifies to \( 6=x - 6 \). Then add 6 to both sides: \( 6 + 6=x-6 + 6 \), so \( x = 12 \).

Step4: Find the length of UW

We know that \( UW=2x - 6 \). Substitute \( x = 12 \) into the formula: \( UW=2\times12-6 \).
First, calculate \( 2\times12 = 24 \), then \( 24-6 = 18 \).

Answer:

18