The balanced and efficient numbers counting conjecture

For an odd integer $n>1$, classify $n$ according to the purely periodic 2-adic expansion of $-1/n$: it is 2-balanced when that period contains equally many $1$s and $0$s, 2-efficient when it contains more $0$s than $1$s, and 2-inefficient when it contains more $1$s than $0$s. Let $B(x)$, $E(x)$, and $I(x)$ count balanced, efficient, and inefficient numbers less than or equal to $x$, respectively.

The balanced and efficient numbers counting conjecture. For all $x$,

$$B(x)+E(x)\geq I(x).$$

The conjecture formalizes the heuristic that inefficient numbers are uncommon, based on a bias toward extra zero digits in finite approximations to the 2-adic expansion of $-1/n$. Its resolution is not supplied in the source.