Question

if st = 4x, tu = x + 17, and su = 6x + 14, what is st? simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Apply segment - addition postulate

Since $SU = ST+TU$, we substitute the given expressions: $6x + 14=4x+(x + 17)$.

Step2: Simplify the right - hand side

$6x + 14=4x+x + 17$, which simplifies to $6x + 14=5x + 17$.

Step3: Solve for x

Subtract $5x$ from both sides: $6x-5x+14=5x-5x + 17$, so $x+14 = 17$. Then subtract 14 from both sides: $x=17 - 14$, and $x = 3$.

Step4: Find the value of ST

Since $ST = 4x$, substitute $x = 3$ into the expression for $ST$. So $ST=4\times3=12$.

Answer:

12