Question

on a line segment, u is between t and v. if tu = x + 9, uv = 6, and tv = 8x + 1, what is tu? simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Apply segment addition postulate

Since \( U \) is between \( T \) and \( V \), we have \( TU + UV = TV \). Substituting the given expressions: \( (x + 9) + 6 = 8x + 1 \).

Step2: Solve for \( x \)

Simplify the left side: \( x + 15 = 8x + 1 \). Subtract \( x \) from both sides: \( 15 = 7x + 1 \). Subtract 1 from both sides: \( 14 = 7x \). Divide by 7: \( x = 2 \).

Step3: Find \( TU \)

Substitute \( x = 2 \) into \( TU = x + 9 \): \( TU = 2 + 9 = 11 \).

Answer:

11