we know that
If Q is the midpoint of the line segment PR
then
[tex]PQ=QR[/tex]
[tex]PR=PQ+QR[/tex]
Step [tex]1[/tex]
Find the value of x
in this problem we have
[tex]PQ=6x+25\\ QR=16-3x[/tex]
substitute in the formula above
[tex]6x+25=16-3x[/tex]
[tex]6x+25=16-3x\\ 6x+3x=16-25\\9x=-9\\x=-1[/tex]
so
[tex]PQ=6x+25=6*(-1)+25=19\ units[/tex]
[tex]QR=16-3*(-1)=19\ units[/tex]
Step [tex]2[/tex]
Find the value of PR
[tex]PR=PQ+QR[/tex]
[tex]PR=19+19=38\ units[/tex]
therefore
the answer is
the value of PR is [tex]38\ units[/tex]
