Question

u is the midpoint of $overline{tv}$. if $tu = 6x$ and $tv = 11x + 3$, what is $tu$?
simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Use mid - point property

Since \(U\) is the mid - point of \(\overline{TV}\), then \(TV = 2TU\). Given \(TU = 6x\) and \(TV=11x + 3\), we have the equation \(11x + 3=2\times(6x)\).

Step2: Solve the equation for \(x\)

Expand the right - hand side: \(11x + 3 = 12x\). Subtract \(11x\) from both sides: \(3=12x−11x\), so \(x = 3\).

Step3: Find the value of \(TU\)

Since \(TU = 6x\), substitute \(x = 3\) into the expression for \(TU\). Then \(TU=6\times3=18\).

Answer:

18