Question

if tu = 3x, uv = x + 4, and tv = 20, what is tu? simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Set up equation based on segment - addition

Since $TV=TU + UV$, we have $3x+(x + 4)=20$.

Step2: Combine like - terms

Combining the $x$ terms on the left - hand side gives $4x+4 = 20$.

Step3: Isolate the variable term

Subtract 4 from both sides: $4x=20 - 4$, so $4x=16$.

Step4: Solve for $x$

Divide both sides by 4: $x=\frac{16}{4}=4$.

Step5: Find the value of $TU$

Since $TU = 3x$, substitute $x = 4$ into the expression for $TU$. So $TU=3\times4 = 12$.

Answer:

12