Confusion on construction of type III factors

Question

Well $G$ is group of translations: $\mathbb{R} \ni s:\mapsto as+b $ where $a, b \in \mathbb{Q}$, modulus of $a\neq1$. Under this action of $G$ on $\mathbb{R}$ why Lebesgue measure is not invariant? Further but which reason restriction of the group only left translations $\mathbb{R} \ni s:\mapsto as$ where $a\in \mathbb{Q}$ the Lebesgue measure is left invariant is not clear to me. Please give hint.