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Sagot :
If M is the midpoint of PQ. MQ = 5x + 8 and PQ = 6x + 56, then PM = 58
Since M is the midpoint of PQ
PM + MQ = PQ................(*)
Given:
PQ = 6x + 56
MQ = 5x + 8
Substitute PQ and MQ into equation (*)
PM + (5x + 8) = 6x + 56
Collect like terms
PM = 6x + 56 - (5x + 8)
Expand the equation using the distributive rule
PM = 6x + 56 - 5x - 8
PM = 6x - 5x + 56 - 8
PM = x + 48.........(**)
Equate MQ and PM
MQ = PM
5x + 8 = x + 48
Collect like terms
5x - x = 48 - 8
4x = 40
Divide both sides by 4
4x / 4 = 40/4
x = 10
Substitute x = 10 into equation (**)
PM = x + 48
PM = 10 + 48
PM = 58
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