Answer:
3 < M - N < 9
Step-by-step explanation:
First, let's write the inequalities for these two numbers.
"a number greater than -3 and less than -2"
-3 < N < -2
"a number greater than 1 and less than 6"
1 < M < 6
We want to subtract the first one to the second one, so we want to get:
M - N
Because this is a subtraction, the lower bound of the subtraction happens when we have the minimum value of M and the maximum value of N.
Then the minimum value of M - N happens when:
M = 1
N = -2
(notice that M can't be equal to 1, and N can't be equal to -2, we just do this to find the lower bound)
Then the lower bound is:
M - N = 1 - (-2) = 3
We already got:
3 < M - N
For the upper bound, we need to find the difference between the largest value of M, and the lowest value of N
This is:
M = 6
N = -3
M - N = 6 - (-3) = 9
Then:
M - N < 9
If we take both of our results, the possible values of the subtraction are given by:
3 < M - N < 9
