Question

d+s ˃ -3

d ˃ -7

find s

it says the answer is 4 (s=4) but it seems not ok because depending on d the number can be pretty much anything

Answer 1

subtract them, (valid since both inequality signs are the same)
d+s - d > -3 - (-7)
s > 4

Answer 2

I don't like that subtraction. Subtracting a larger value gives a smaller result. For example, suppose we have small x > 0

d = -7+x > -7

d+s = -7+x+s > -3
x+s > 4
s > 4-x

So, suppose x = .1, and thus
d = -7+.1 = -6.9
If s > 4-.1 = 3.9, ok, since d+s > -3

If s = 3.99, d+s = -6.9+3.99 = -2.91

So, we don't have to have s>4, as long as it's closer to 4 than d is to -7.

Answer 3

let d = -6.9, valid for d > -7
-6.9+s > -3
s > 3.9 which is NOT s > 4

Yup, Steve is right, we have one exception which rules out my entire solution.