Question

point t is on line segment \\( \overline{su} \\). given \\( su = 4x + 1 \\), \\( tu = 3x \\), and \\( st = 3x - 1 \\), determine the numerical length of \\( \overline{su} \\).

Explanation:

Step1: Use segment addition postulate

Since T is on \( \overline{SU} \), we have \( ST + TU = SU \). Substituting the given expressions: \( (3x - 1) + 3x = 4x + 1 \).

Step2: Solve for x

Combine like terms: \( 6x - 1 = 4x + 1 \). Subtract \( 4x \) from both sides: \( 2x - 1 = 1 \). Add 1 to both sides: \( 2x = 2 \). Divide by 2: \( x = 1 \).

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

Substitute \( x = 1 \) into \( SU = 4x + 1 \): \( SU = 4(1) + 1 = 5 \).

Answer:

5