Let $a_1,a_2 \in \mathbb{Q}:a_1≥1,a_2≥1$. What should be the minimum value of $x\in\mathbb{R}$: $n∈[1,x]$ to ensure that $4k−3≤na_1≤4k−1$ such that $k∈N$ and $4l−3≤na_2≤4l−1$ such that $l∈N$?

Numerical computations suggest the answer to this is $3$ but I'm out of ideas how to prove this formally.

Let $a_1,a_2 \in \mathbb{Q}:a_1≥1,a_2≥1$. What should be the minimum value of $x\in\mathbb{R}$: $n∈[1,x]$ to ensure that $4k−3≤na_1≤4k−1$ such that $k∈N$ and $4l−3≤na_2≤4l−1$ such that $l∈N$ for all $a_1, a_2$?

Numerical computations suggest the answer to this is $3$ but I'm out of ideas how to prove this formally.

Let $a_1,a_2 \in \mathbb{Q}:a_1≥1,a_2≥1$. What should be the maximum value of $n∈\mathbb{R}:n≥1$ to ensure that $4k−3≤na_1≤4k−1$ such that $k∈N$ and $4l−3≤na_2≤4l−1$ such that $l∈N$?

Numerical computations suggest the answer to this is $3$ but I'm out of ideas how to prove this formally.

Let $a_1,a_2 \in \mathbb{Q}:a_1≥1,a_2≥1$. What should be the minimum value of $x\in\mathbb{R}$: $n∈[1,x]$ to ensure that $4k−3≤na_1≤4k−1$ such that $k∈N$ and $4l−3≤na_2≤4l−1$ such that $l∈N$?

Numerical computations suggest the answer to this is $3$ but I'm out of ideas how to prove this formally.