Question

G is a set of all natural number except -1 defined by a*b = + b+ ab for all a, b $\in$ G in this group (G , *) , the solution of $2^{-1}\ast x\ast 3^{-1}=5$

Answer 1

$a\ast b=+b+ab$

$2^{-1}\ast x\ast 3^{-1}=(+x+2^{-1}x)\ast 3^{-1}=\frac{3}{2}x\ast 3^{-1}=3^{-1}+\frac{x}{2}=5$

$\frac{x}{2}=\frac{14}{3}⟹x=\frac{28}{3}$