Question

u is a point on segment (overline{tv}). if (tu = 6x + 10), (uv = 4x), and (tv = 11x - 8), what is (tu)? simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Use segment addition postulate

Since \( U \) is on \( \overline{TV} \), we have \( TU + UV = TV \). Substituting the given expressions: \( (6x + 10) + 4x = 11x - 8 \).

Step2: Simplify and solve for \( x \)

Combine like terms: \( 10x + 10 = 11x - 8 \). Subtract \( 10x \) from both sides: \( 10 = x - 8 \). Add 8 to both sides: \( x = 18 \).

Step3: Find \( TU \)

Substitute \( x = 18 \) into \( TU = 6x + 10 \): \( TU = 6(18) + 10 = 108 + 10 = 118 \).

Answer:

118