Question

point t is on line segment \\( \overline{su} \\). given \\( su = 5x \\), \\( tu = 2x \\), and \\( st = 4x - 3 \\), determine the numerical length of \\( \overline{tu} \\).

Explanation:

Step1: Apply segment addition postulate

Since T is on segment SU, we have \( ST + TU = SU \). Substituting the given expressions: \( (4x - 3) + 2x = 5x \).

Step2: Solve for x

Combine like terms: \( 6x - 3 = 5x \). Subtract \( 5x \) from both sides: \( x - 3 = 0 \). Then add 3 to both sides: \( x = 3 \).

Step3: Find length of TU

Substitute \( x = 3 \) into \( TU = 2x \): \( TU = 2(3) = 6 \).

Answer:

6