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M is the midpoint of PQ. MQ = 5x + 8 and PQ = 6x + 56, find PM.

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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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