Question

if ( tu = 7 ), ( uv = x + 5 ), and ( tv = 3x - 18 ), what is ( tv )?
simplify your answer and write it as a proper fraction, mixed number, or integ

Explanation:

Step1: Use segment addition postulate

According to the segment addition postulate, \(TU + UV=TV\).
Substitute the given expressions: \(7+(x + 5)=3x-18\).

Step2: Simplify the left - hand side

Simplify \(7+(x + 5)\) to \(x+12\). So the equation becomes \(x + 12=3x-18\).

Step3: Solve for \(x\)

Subtract \(x\) from both sides: \(12=3x-x - 18\), which simplifies to \(12 = 2x-18\).
Add \(18\) to both sides: \(12 + 18=2x\), so \(30 = 2x\).
Divide both sides by \(2\): \(x=\frac{30}{2}=15\).

Step4: Find \(TV\)

Substitute \(x = 15\) into the expression for \(TV\) (\(TV=3x-18\)).
\(TV=3\times15-18\).
First, calculate \(3\times15 = 45\). Then \(45-18=27\).

Answer:

\(27\)