Question

if uv = 17, vw = 3x + 10, and uw = 5x + 7, what is vw?
diagram: u---v---w with uv labeled 17, vw labeled 3x + 10, uw labeled 5x + 7
simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Apply segment addition postulate

From the diagram, \( UW = UV + VW \). Substitute the given expressions: \( 5x + 7 = 17 + 3x + 10 \).

Step2: Solve for \( x \)

Simplify the right - hand side: \( 5x + 7 = 3x + 27 \). Subtract \( 3x \) from both sides: \( 5x-3x + 7=3x - 3x+ 27 \), which gives \( 2x+7 = 27 \). Then subtract 7 from both sides: \( 2x+7 - 7=27 - 7 \), so \( 2x = 20 \). Divide both sides by 2: \( x=\frac{20}{2}=10 \).

Step3: Find \( VW \)

Substitute \( x = 10 \) into the expression for \( VW \), which is \( 3x + 10 \). So \( VW=3\times10 + 10=30 + 10 = 40 \).

Answer:

\( 40 \)