Question

if (tu = 11x + 10), (uv = 6x + 14), and (tv = 18x + 15), what is (tu)?
simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Use segment - addition postulate

Since $TV=TU + UV$, we substitute the given expressions: $(11x + 10)+(6x + 14)=18x + 15$.

Step2: Combine like - terms on the left - hand side

$11x+6x + 10 + 14=18x + 15$, which simplifies to $17x+24 = 18x + 15$.

Step3: Solve for x

Subtract $17x$ from both sides: $24=x + 15$. Then subtract 15 from both sides to get $x=24 - 15=9$.

Step4: Find the value of TU

Substitute $x = 9$ into the expression for $TU$. $TU=11x + 10=11\times9+10=99 + 10=109$.

Answer:

109