Question

if st = 5x, tu = 10, and su = 12x + 3, what is st? diagram: s---t----u with st labeled 5x, tu labeled 10, su labeled 12x + 3 simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Apply segment addition postulate

From the diagram, \( SU = ST + TU \). Substitute the given expressions: \( 12x + 3 = 5x + 10 \).

Step2: Solve for \( x \)

Subtract \( 5x \) from both sides: \( 12x - 5x + 3 = 10 \) → \( 7x + 3 = 10 \).
Subtract 3 from both sides: \( 7x = 10 - 3 \) → \( 7x = 7 \).
Divide by 7: \( x = \frac{7}{7} = 1 \).

Step3: Find \( ST \)

Given \( ST = 5x \), substitute \( x = 1 \): \( ST = 5(1) = 5 \).

Answer:

\( 5 \)