In Sakurai's Modern Quantum Mechanics, p.270, he wrote an equation the parity transformation $\pi$ (where $\pi = \pi^\dagger = \pi^{-1}$) as $$\pi \left(1- \frac{i p \cdot d x'}{\hbar}\right) \pi^\dagger = \left(1+ \frac{i p \cdot d x'}{\hbar}\right). \tag{0}$$
How is this consistent with these two equations (4.2.3) and (4.2.10) also derived:
$$ \pi x' \pi^\dagger = -x' \tag{1} $$
$$ \pi p \pi^\dagger = -p \tag{2} $$
Is that $$\pi dx' \pi^\dagger = dx' \tag{3} $$
$$\pi (p \cdot dx') \pi^\dagger = -( p \cdot dx' ) \tag{4} $$
How to understand the Eq. 1 versus Eq. 3? but how to understand the Eqs. 1, 2, versus Eq. 4?
Naively, it seems that
$$ \pi dx' \pi^\dagger = - dx' \tag{5},$$
because say $dx'=(x_A- x_B)$ is the spatial interval difference between two points on $A$ and $B$, then $$\pi dx' \pi^\dagger=\pi \Delta x \pi^\dagger=\pi (x_A- x_B) \pi^\dagger =(-x_A- (-x_B))=-(x_A- x_B)=-dx'.$$ Also I thought: $$ \pi (p \cdot dx') \pi^\dagger = +( p \cdot dx' ) \tag{6} $$
Could you correct me why Eqs. 3 and 4 are correct, but Eqs. 5 and 6 are not?