Question

u is the midpoint of (overline{tv}). if (tu = 5x) and (uv = x + 4), what is (tu)?

t ---- u ---- v
5x x + 4

simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Use midpoint property

Since \( U \) is the midpoint of \( \overline{TV} \), \( TU = UV \). So we set up the equation \( 5x = x + 4 \).

Step2: Solve for \( x \)

Subtract \( x \) from both sides: \( 5x - x = x + 4 - x \), which simplifies to \( 4x = 4 \). Then divide both sides by 4: \( x = \frac{4}{4} = 1 \).

Step3: Find \( TU \)

Substitute \( x = 1 \) into \( TU = 5x \), so \( TU = 5\times1 = 5 \).

Answer:

\( 5 \)