Ok, I'll try to explain my solution as best as I could.
If clarifications are needed, please do not hesitate.
We are given that both p and q are integers (i.e. positive, negative whole numbers or zero).
We will assume, without loss of generality, that
******* p >= q ********* .....................(1)
and in return, we have to make sure the inequalities have to be satisfied for BOTH p and q, because we don't know if q is actually greater than p.
Question says the positive difference between p and q is no more than 3. Expressed in an inequality,
p-q ≤ 3 ............................................(2)
Also, the sum of p and q must be between -12 and 30.
So
p+q ≥ -12 .......................................(3)
and
p+q <= 30 ..........................................(4)
Rewrite (2) as p ≤ q+3…………..(2a)
and substitute (2a) in (4)
q+q+3 ≤ 30 => 2q ≤ 30-3 => 2q ≤ 27 => q ≤ 13.5 =>
q ≤ 13 ………………………(5) because q is an integer.
Put (5) in (2a)
p ≤ 13+3 = 16
So the upper limit of p or q is 16.
Similarly,
Rewrite (2) as q ≥ p-3…………..(2b)
And substitute in (3),
p+(p-3) ≥ -12 => p+p ≥ -12+3 => 2p ≥ -9 => p ≥ -4.5 =>
p ≥ -4 ……………………(6) because p is an integer, and -4 >-4.5
Put (6) back in (2b)
q ≥ (-4) -3, or q ≥ -7
So the combined lower limit of p and q is -7
If we set Q = either (our) p or q, then
-7 ≤ Q ≤ 16
Author's note To whom it may concern:
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