Answer
The minimum value is $3$, and the maximum value is $11$.
Work Step by Step
Recall two properties: $1) |a|-|b| \leq |a+b| \leq |a|+|b| \\ 2) |a|-|b| \leq |a-b| \leq |a|+|b|$
From property-1, we can write $|7-4| \leq |a+b| \leq 7+4\\3 \leq |a+b| \leq 11$
From property-2, we can write $|7-4| \leq |a-b| \leq 7+4\\3 \leq |a-b| \leq 11$
The minimum value is $3$, and the maximum value is $11$.
