Question

t is a point on segment \\(\overline{su}\\). if \\(st = 11\\), \\(tu = 14x - 1\\), and \\(su = 6x + 18\\), what is \\(tu\\)? simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Use segment addition postulate

Since \( T \) is on \( \overline{SU} \), we have \( ST + TU = SU \). Substituting the given expressions: \( 11 + (14x - 1) = 6x + 18 \)

Step2: Simplify and solve for \( x \)

Simplify left side: \( 11 + 14x - 1 = 14x + 10 \). So equation is \( 14x + 10 = 6x + 18 \). Subtract \( 6x \) and \( 10 \) from both sides: \( 14x - 6x = 18 - 10 \) → \( 8x = 8 \) → \( x = 1 \)

Step3: Find \( TU \)

Substitute \( x = 1 \) into \( TU = 14x - 1 \): \( TU = 14(1) - 1 = 13 \)

Answer:

\( 13 \)