Question

Q is the midpoint of line segment PR. PQ=6x+25 and QR=16-3x; find PR

Answer 1

we know that

If Q is the midpoint of the line segment PR

then

`PQ=QR`

`PR=PQ+QR`

Step
`1`

Find the value of x

in this problem we have

`PQ=6x+25\\ QR=16-3x`

substitute in the formula above

`6x+25=16-3x`

`6x+25=16-3x\\ 6x+3x=16-25\\9x=-9\\x=-1`

so

`PQ=6x+25=6*(-1)+25=19\ units`

`QR=16-3*(-1)=19\ units`

Step
`2`

Find the value of PR

`PR=PQ+QR`

`PR=19+19=38\ units`

therefore

the answer is

the value of PR is
`38\ units`