Question

directions: suppose q is the mid - point of pr. use the information to find the missing value. 13. pq = 5x + 14 and qr = 2x - 10; find x. 14. pq = 2x + 1 and qr = 5x - 44; find pq. 15. pq = 6x + 25 and qr = 16 - 3x; find pr. 16. pr = 9x - 31 and qr = 43; find x.

Explanation:

Step1: Use mid - point property

Since Q is the mid - point of PR, PQ = QR.

Step2: Solve for x in 13

Set 5x + 14=2x - 10, then 5x - 2x=-10 - 14, 3x=-24, x = - 8.

Step3: Solve for PQ in 14

Set 2x + 1=5x - 44, 44 + 1=5x - 2x, 3x = 45, x = 15. Then PQ=2x + 1=2×15 + 1=31.

Step4: Solve for x in 15

Set 6x + 25=16 - 3x, 6x+3x=16 - 25, 9x=-9, x=-1. Then PR = PQ + QR=(6x + 25)+(16 - 3x)=3x + 41=3×(-1)+41 = 38.

Step5: Solve for x in 16

Since Q is mid - point, PR = 2QR. So 9x - 31=2×43, 9x - 31 = 86, 9x=86 + 31, 9x=117, x = 13.

Answer:

1. x = - 8
2. PQ = 31
3. PR = 38
4. x = 13