Question

t is the midpoint of $overline{su}$. if $tu = 2x$ and $su = 3x + 2$, what is $su?
s——————t——————u
2x
3x + 2
simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Use mid - point property

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

Step2: Solve the equation for \(x\)

\[

$$\begin{align*} 3x + 2&=4x\\ 4x-3x&=2\\ x&=2 \end{align*}$$

\]

Step3: Find the value of \(SU\)

Substitute \(x = 2\) into the expression for \(SU\). Since \(SU=3x + 2\), then \(SU=3\times2+2=6 + 2=8\).

Answer:

8