Question

1. if t is the midpoint of $overline{su}$, find x.

s 8x + 11 t 12x - 1 u

Explanation:

Step1: Set up equation using mid - point property

Since \(T\) is the mid - point of \(\overline{SU}\), then \(ST = TU\). So, \(8x + 11=12x - 1\).

Step2: Isolate \(x\) terms

Subtract \(8x\) from both sides: \(8x+11 - 8x=12x - 1-8x\), which simplifies to \(11 = 4x-1\).

Step3: Solve for \(x\)

Add 1 to both sides: \(11 + 1=4x-1 + 1\), getting \(12 = 4x\). Then divide both sides by 4: \(\frac{12}{4}=\frac{4x}{4}\), so \(x = 3\).

Answer:

\(x = 3\)