Question

Q is the midpoint of line segment PR. PR=9x-31 and QR=43 ; find x

Answer 1

notice that, if Q is the midpoint of PR, that simply means that PQ = QR = 43.

$\bf \boxed{P}\underset{\leftarrow 9x-31 \to }{\stackrel{\stackrel{\downarrow }{43}}{\rule[0.35em]{10em}{0.25pt}}Q\stackrel{43}{\rule[0.35em]{10em}{0.25pt}}}\boxed{R} \\\\\\ 9x-31=43+43\implies 9x-31=86\implies 9x=117 \\\\\\ x=\cfrac{117}{9}\implies x=13$