Question

t is the midpoint of su. if tu = x + 4 and su = 3x + 4, what is tu? simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Recall mid - point property

Since T is the mid - point of SU, then $SU = 2\times TU$.

Step2: Set up the equation

We know that $SU=3x + 4$ and $TU=x + 4$, and $SU = 2\times TU$. So, $3x+4=2(x + 4)$.

Step3: Expand the right - hand side

Using the distributive property $a(b + c)=ab+ac$, we have $3x+4 = 2x+8$.

Step4: Solve for x

Subtract $2x$ from both sides: $3x-2x+4=2x-2x + 8$, which simplifies to $x+4=8$. Then subtract 4 from both sides: $x=8 - 4=4$.

Step5: Find TU

Substitute $x = 4$ into the expression for TU. Since $TU=x + 4$, then $TU=4 + 4=8$.

Answer:

8