Question

if $st = 3x$, $tu = 8x - 17$, and $su = 7x + 11$, what is $tu$? 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 \( ST + TU = SU \). Substituting the given expressions: \( 3x + (8x - 17) = 7x + 11 \).

Step2: Simplify and solve for \( x \)

Combine like terms on the left: \( 11x - 17 = 7x + 11 \). Subtract \( 7x \) from both sides: \( 4x - 17 = 11 \). Add 17 to both sides: \( 4x = 28 \). Divide by 4: \( x = 7 \).

Step3: Find \( TU \)

Substitute \( x = 7 \) into \( TU = 8x - 17 \): \( TU = 8(7) - 17 = 56 - 17 = 39 \).

Answer:

39