Given that Q and R are midpoints, then segment QR is half of segment MP.
[tex]QR=\frac{1}{2}MP[/tex]Substituting with data,
[tex]\begin{gathered} 76-8x=\frac{1}{2}(89-9x) \\ 76-8x=\frac{1}{2}\cdot89-\frac{1}{2}9x \\ 76-8x=\frac{89}{2}-\frac{9}{2}x \\ 76-\frac{89}{2}=-\frac{9}{2}x+8x \\ \frac{76\cdot2-89}{2}=\frac{-9+8\cdot2}{2}x \\ \frac{63}{2}=\frac{7}{2}x \\ \frac{63}{2}\cdot\frac{2}{7}=x \\ 9=x \end{gathered}[/tex]Therefore, the measure of MP is:
MP = 89 - 9x
MP = 89 - 9*9
MP = 89 - 81
MP = 8
