Answer
$$\overline x = \frac{{18}}{5}$$
Work Step by Step
$$\eqalign{
& {m_1} = 8,{\text{ }}{m_2} = 12,{\text{ }}{m_3} = 6,{\text{ }}{m_4} = 14 \cr
& {\text{Located at }} \cr
& {x_1} = - 1,{\text{ }}{x_2} = 2,{\text{ }}{x_3} = 5,{\text{ }}{x_4} = 7 \cr
& {\text{The moment about the origin is }} \cr
& {M_0} = {m_1}{x_1} + {m_2}{x_2} + {m_3}{x_3} + {m_4}{x_4} \cr
& {M_0} = \left( 8 \right)\left( { - 1} \right) + \left( {12} \right)\left( 2 \right) + \left( 6 \right)\left( 5 \right) + \left( {14} \right)\left( 7 \right) \cr
& {M_0} = 144 \cr
& m{\text{ is the total mass of the system}} \cr
& m = {m_1} + {m_2} + {m_3} + {m_4} \cr
& m = 8 + 12 + 6 + 14 \cr
& m = 40 \cr
& {\text{The center of mass is }}\overline x = \frac{{{M_0}}}{m}{\text{, then}} \cr
& \overline x = \frac{{144}}{{40}} \cr
& \overline x = \frac{{18}}{5} \cr} $$
