Find the value of XP if X is between P and Q.

XQ = 3k, XP = 7k - 2, PQ = 6k + 18

If X is between P and Q, then PQ is the whole line segment and XQ and XP are line segments that add up to PQ. Therefore, you can make an equation where XQ and XP add up to PQ.

XQ + XP = PQ

(3k) + (7k - 2) = 6k + 18

Combine like terms.

10k - 2 = 6k + 18

Add 2 to both sides.

10k = 6k + 20

Subtract 6k from both sides.

4k = 20

Divide both sides by 4.

k = 5

Plug 5 for k into XP.

XP = 7 (5) - 2 ⇒ 35 - 2

XP = 33

3k+7k-2 = 6k+18

10k - 2 = 6k + 18

4k = 20

k=5

XP = 35-2 = 33