1. ## linear inequality

I got this problem from a guide book.

Question:
It is given that $-5\le p\le 2$ and $3\le q \le 10$.
Find the least posible value of $\frac{q-p}{q}$

Answer given in the book is as follows:
Least possible value $\frac{q-p}{q}=\frac{3-2}{10}=\frac{1}{10}$

My question is how can the variable q takes two different values in an algebraic expression.

2. I don't know how $q$ can take two different values but I have a solution :
$\frac {q-p}q=1-\frac pq$ So we need to maximize $\frac pq$. And $\frac pq$ has its maximum when $p$ is the largest possible and $q$ is the least possible. So $p=2$ and $q=3$: $\frac {q-p}q=\frac {3-2}{3}=\mathbf{\frac 13}$