Question

on a line segment, u is between t and v. if tu = 13x, uv = 10x - 11, and tv = 16x + 17, 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: \( 13x + (10x - 11) = 16x + 17 \).

Step2: Simplify and solve for \( x \)

Combine like terms: \( 23x - 11 = 16x + 17 \). Subtract \( 16x \) from both sides: \( 7x - 11 = 17 \). Add 11 to both sides: \( 7x = 28 \). Divide by 7: \( x = 4 \).

Step3: Find \( TU \)

Substitute \( x = 4 \) into \( TU = 13x \): \( TU = 13 \times 4 = 52 \).

Answer:

52