Question

point t is on line segment \\(overline{su}\\). given \\(tu = x - 1\\), \\(su = 3x - 7\\), and \\(st = x + 7\\), determine the numerical length of \\(overline{tu}\\).

Explanation:

Step1: Use segment addition postulate

Since T is on \( \overline{SU} \), \( ST + TU = SU \). Substitute the given expressions: \( (x + 7) + (x - 1) = 3x - 7 \).

Step2: Simplify and solve for x

Simplify left side: \( 2x + 6 = 3x - 7 \). Subtract \( 2x \) from both sides: \( 6 = x - 7 \). Add 7 to both sides: \( x = 13 \).

Step3: Find length of \( \overline{TU} \)

Substitute \( x = 13 \) into \( TU = x - 1 \): \( TU = 13 - 1 = 12 \).

Answer:

12