Question

Point N is on line segment MO. Given MO = 3x - 10, NO = x, and MN = 8,

determine the numerical length of MO.

Answer 1

`\underset{\leftarrow \qquad 3x - 10\qquad \to }{M\stackrel{8}{\rule[0.35em]{10em}{0.25pt}} N\stackrel{x}{\rule[0.35em]{15em}{0.25pt}} O} \\\\\\ \stackrel{MO}{3x-10}~~ = ~~\stackrel{MN}{8}~~ + ~~\stackrel{NO}{x}\implies 2x-10=8\implies 2x=18\implies x=\cfrac{18}{2} \\\\\\ \boxed{x=9}\hspace{5em}\stackrel{\textit{\LARGE MO}}{3x-10\implies 3(9)-10\implies 17}`