Find the interval of all $x$ such that both $2x$ and $3x$ are in the interval $(1,2)$.
1 < 2x < 2 divide through by 2
1/2 < x < 1
Also
1 < 3x < 2 divide through by 3
1/3 < x < 2/3
We need the most restrictive interval that solves both of these inequalities....this is (1/2 , 2/3)
