Question

if st = x + 12, tu = 11x, and su = 14x + 6, what is tu? simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Use segment - addition postulate

Since $SU=ST + TU$, we substitute the given expressions: $(x + 12)+11x=14x + 6$.

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

$x+11x + 12=14x + 6$, which simplifies to $12x+12 = 14x+6$.

Step3: Isolate the variable terms

Subtract $12x$ from both sides: $12x - 12x+12=14x-12x + 6$, resulting in $12 = 2x+6$.

Step4: Solve for $x$

Subtract 6 from both sides: $12 - 6=2x+6 - 6$, so $6 = 2x$. Then divide both sides by 2: $x = 3$.

Step5: Find the value of $TU$

Since $TU = 11x$, substitute $x = 3$ into the expression. So $TU=11\times3=33$.

Answer:

33