Here's an approach that uses a nice rule that essentially says: "if two inequalities are arranged so that the inequality symbols are facing the same direction, we can ADD them to create a new inequality.

We have: 5 ≥ a > 1, which we'll rewrite as 1 < a ≤ 5
Now, for the time being, let's focus on the fact that a ≤ 5

We're also told that b ≥ – 2
To get the inequality facing the same way as the above inequality (in red), let's take b ≥ – 2 and multiply both sides by -1
When we do this, we get: -b ≤ 2

Great, we now have:
a ≤ 5
-b ≤ 2

Since the inequality symbols are facing the same direction, we can ADD the inequalities to create a new inequality.
When we do so, we get: a - b ≤ 7
This means that a - b CANNOT equal 8

So, the correct answer is E

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Hi

If we look at a-b, b is infinite on the upper side since b>=2...
And B is being subtracted, so the minimum value will be infinite..
this itself should tell us that the largest value should be the answer ..

But let's see why 8 should be the answer..
Max value of a and min value of b should give us max value..
a has max value of 5 and min value of b is -2..
So a-b=5-(-2)=5+2=7..
So any value beyond 7 will be wrong..

Therefore 8 is not possible..

E
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value of a 5,4,3,2,1 and that of b ; -2,-1,0,1,2,3...
A. –5 ; 5-10
B. –3 ; 5-8
C. 2 ; 5-3
D. 7 ; 5- (-2)
E. 8 ; 5- ( -3) which is not part of b correct choice
option E

Let's use number line to solve these kind of questions:

XXXXXXXXXXX.________. <=values of a (1,5)
----(-2)--------1-----------5
XXXX._______________________________________......<= values of b (-2, inf)

a-b is the distance between a and b
Let's find the min/max to find the range.

min. difference = 1-(-2)
max. positive difference = 5-(-2) =7
max. negative difference can be infinity = 2-10^5 or even bigger than this (as b>=-2)

So, the expression has range [3,7] union [-infinity, 0]
So, Answer is E

Please give kudos if it helped you

We can find the MIN and MAX Range of (a - b)

We are given that the Variables a and b MUST be Integers:

Therefore:

2 </= a </= 5

-(2) </= b </= +Infinite


1st) MAXIMIZE Expression (a - b) ---- In order to do this, we want the MAX a we can get and the MIN b we can get

MAX a = +5
MIN b = -(2)

Maximum Bound of (a - b) = +5 - -(2) = +5 + 2 = +7

Therefore, the Value of (a - b) can NOT go beyond +7


-E- 8 ---- can NOT be a Value of (a - b)