Question

use the figure to the right to find the value of pt. pt = 5x + 2 and tq = 7x - 8. pt = (simplify your answer)

Explanation:

Assuming \( T \) is the midpoint of \( PQ \), so \( PT = TQ \).

Step1: Set \( PT = TQ \)

\( 5x + 2 = 7x - 8 \)

Step2: Solve for \( x \)

Subtract \( 5x \) from both sides: \( 2 = 2x - 8 \)
Add 8 to both sides: \( 10 = 2x \)
Divide by 2: \( x = 5 \)

Step3: Find \( PT \)

Substitute \( x = 5 \) into \( PT = 5x + 2 \):
\( PT = 5(5) + 2 = 25 + 2 = 27 \)

Answer:

27