Answer:
x = 6
Step-by-step explanation:
Given that PQ = 3x + 14, QR = 7x - 10, and Q is the midpoint of PR, it means Q is equidistant from both endpoints of P and Q. In order words, the distance from P to Q is the same as the distance from Q to R.
Therefore, PQ = QR. Which is:
[tex] 3x + 14 = 7x - 10 [/tex]
Solve for x. Collect like terms
[tex] 3x -7x = - 14 - 10 [/tex]
[tex] -4x = -24 [/tex]
Divide both sides by -4x
[tex] x = 6 [/tex]
