Question

if st = 11x + 17, tu = 7x − 19, and su = 19x − 19, what is tu?
diagram: s---t---u with st labeled 11x + 17, tu labeled 7x − 19, su labeled 19x − 19
simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Apply segment addition postulate

Since \( S \), \( T \), \( U \) are collinear with \( T \) between \( S \) and \( U \), we have \( ST + TU = SU \). Substitute the given expressions:
\( (11x + 17) + (7x - 19) = 19x - 19 \)

Step2: Simplify left - hand side

Combine like terms: \( 11x+7x + 17-19=18x - 2 \). So the equation becomes \( 18x - 2=19x - 19 \)

Step3: Solve for \( x \)

Subtract \( 18x \) from both sides: \( - 2=x - 19 \). Then add 19 to both sides: \( x=19 - 2 = 17 \)

Step4: Find \( TU \)

Substitute \( x = 17 \) into the expression for \( TU \), which is \( 7x-19 \). So \( TU=7\times17-19 \)
Calculate \( 7\times17 = 119 \), then \( 119-19 = 100 \)

Answer:

\( 100 \)