Question

if uv = x - 8, vw = 7, and uw = 2x - 17, what is uw? diagram of u---v---w with uv labeled x - 8, vw labeled 7, uw labeled 2x - 17 simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Use segment addition postulate

From the number line, we know that \( UV + VW = UW \). Substituting the given expressions, we get \((x - 8)+7 = 2x - 17\).

Step2: Simplify and solve for x

Simplify the left side: \(x - 8 + 7=x - 1\). So the equation becomes \(x - 1 = 2x - 17\). Subtract \(x\) from both sides: \(-1=x - 17\). Then add 17 to both sides: \(x = 16\).

Step3: Find UW

Substitute \(x = 16\) into the expression for \(UW\), which is \(2x - 17\). So \(UW=2(16)-17 = 32 - 17 = 15\).

Answer:

15