Question

if uv = 6, vw = 10x - 1, and uw = 15x, what is uw? simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Use segment - addition postulate

Since $UW=UV + VW$, we substitute the given expressions: $15x=6+(10x - 1)$.

Step2: Simplify the right - hand side of the equation

$15x=6 + 10x-1$, which simplifies to $15x=10x + 5$.

Step3: Solve for x

Subtract $10x$ from both sides: $15x-10x=10x + 5-10x$, so $5x=5$. Then divide both sides by 5: $x = 1$.

Step4: Find the value of UW

Since $UW = 15x$ and $x = 1$, then $UW=15\times1=15$.

Answer:

15