Question

if st = 16, tu = x + 14, and su = 2x + 17, what is su? 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 can substitute the given expressions: $2x + 17=16+(x + 14)$.

Step2: Simplify the right - hand side

$16+(x + 14)=x+(16 + 14)=x + 30$. So the equation becomes $2x+17=x + 30$.

Step3: Solve for x

Subtract x from both sides: $2x - x+17=x - x + 30$, which simplifies to $x+17 = 30$. Then subtract 17 from both sides: $x=30 - 17$, so $x = 13$.

Step4: Find SU

Substitute $x = 13$ into the expression for $SU$. $SU=2x+17=2\times13 + 17$. First, calculate $2\times13=26$, then $26+17 = 43$.

Answer:

43