Question

on a line segment, t is between s and u. if st = 10, tu = x + 10, and su = 2x + 4, what is tu? simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Apply segment addition postulate

Since \( T \) is between \( S \) and \( U \), we have \( ST + TU = SU \). Substituting the given values: \( 10+(x + 10)=2x + 4 \).

Step2: Simplify and solve for \( x \)

Simplify the left - hand side: \( 10+x + 10=2x + 4\), which becomes \( x+20 = 2x + 4 \).
Subtract \( x \) from both sides: \( 20=x + 4 \).
Subtract 4 from both sides: \( x=20 - 4=16 \).

Step3: Find the length of \( TU \)

We know that \( TU=x + 10 \), substitute \( x = 16 \) into the expression for \( TU \): \( TU=16 + 10=26 \).

Answer:

\( 26 \)