Question

if uv = 19, vw = x + 16, and uw = 3x + 7, what is vw?
diagram: u---v---w with uv labeled 19, vw labeled x + 16, uw labeled 3x + 7
simplify your answer and write it as a proper fraction, mixed number, or integer.
submit

Explanation:

Step1: Apply segment addition postulate

From the diagram, \( UW = UV + VW \). Substitute the given values: \( 3x + 7 = 19 + (x + 16) \)

Step2: Solve for \( x \)

Simplify the right - hand side: \( 3x + 7 = x + 35 \)
Subtract \( x \) from both sides: \( 3x - x+7=x - x + 35\), which gives \( 2x+7 = 35 \)
Subtract 7 from both sides: \( 2x+7 - 7=35 - 7\), so \( 2x = 28 \)
Divide both sides by 2: \( x=\frac{28}{2}=14 \)

Step3: Find \( VW \)

Since \( VW=x + 16 \), substitute \( x = 14 \): \( VW=14 + 16=30 \)

Answer:

\( 30 \)