Question

if ( tu = x + 9 ), ( uv = 5 ), and ( tv = 8x ), what is ( tu )?
simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Use segment addition postulate

According to the segment addition postulate, \(TU + UV=TV\).
Substitute the given expressions: \((x + 9)+5 = 8x\).

Step2: Simplify the left - hand side

Combine like terms: \(x+14 = 8x\).

Step3: Solve for \(x\)

Subtract \(x\) from both sides: \(14=8x - x\), so \(14 = 7x\).
Divide both sides by \(7\): \(x=\frac{14}{7}=2\).

Step4: Find \(TU\)

Since \(TU=x + 9\) and \(x = 2\), then \(TU=2 + 9\).

Answer:

\(11\)