The value of x is 13.
Given,
Q is the midpoint of P and R.
PR = 9x - 31 and QR = 43
We need to find the value of x.
We have,
<------9x - 31-------------->
P_______Q_______R
<-----43------>
Since Q is the midpoint of P and R.
PQ = QR = PR/2
Now,
QR = PR/2
43 = (9x - 31) / 2
Multiplying 2 on both sides
43 x 2 = 9x - 31
86 = 9x - 31
Adding 31 on both sides
86 + 31 = 9x - 31 + 31
117 = 9x
Dividing by 9 into both sides
117/9 = 9x/9
13 = x
x = 13
Thus the value of x is 13.
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