Question

point u is on line segment (overline{tv}). given (tv = x + 10), (tu = 3x - 8), and (uv = 10), determine the numerical length of (overline{tv}).

Explanation:

Step1: Use segment addition postulate

Since \( U \) is on \( \overline{TV} \), we have \( TU + UV = TV \). Substituting the given expressions: \( (3x - 8) + 10 = x + 10 \).

Step2: Simplify and solve for \( x \)

Simplify left side: \( 3x + 2 = x + 10 \). Subtract \( x \) from both sides: \( 2x + 2 = 10 \). Subtract 2: \( 2x = 8 \). Divide by 2: \( x = 4 \).

Step3: Find length of \( TV \)

Substitute \( x = 4 \) into \( TV = x + 10 \): \( TV = 4 + 10 = 14 \).

Answer:

14