Question

if t is the midpoint of $overline{su}$, find the value of $x$. the diagram is not to scale.
$8x + 11$ $12x - 1$
s t u
(a) $x = 3$
(b) $x = 2$
(c) $x = 4$
(d) $x = 5$

Explanation:

Step1: Use mid - point property

Since T is the mid - point of $\overline{SU}$, then $ST = TU$. So, we set up the equation $8x + 11=12x - 1$.

Step2: Isolate x terms

Subtract $8x$ from both sides of the equation: $8x+11 - 8x=12x - 1-8x$, 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:

A. $x = 3$