For the product of two numbers to be less than or equal to zero:
1) either one can be zero; thus, s = -4 or s = 3.
2) the first one is negative and the second one is positive:
x + 4 < 0 and s - 3 > 0
so: x < -4 and x > 3 (but this situation isn't possible)
3) the first one is positive and the second one is negative:
x + 4 > 0 and s - 3 < 0
so: x > -4 and x < 3 (this situation is possible)
Thus, the answer (from part 1 and part 3): -4 ≤ x ≤ 3
For the product of two numbers to be less than or equal to zero:
1) either one can be zero; thus, s = -4 or s = 3.
2) the first one is negative and the second one is positive:
x + 4 < 0 and s - 3 > 0
so: x < -4 and x > 3 (but this situation isn't possible)
3) the first one is positive and the second one is negative:
x + 4 > 0 and s - 3 < 0
so: x > -4 and x < 3 (this situation is possible)
Thus, the answer (from part 1 and part 3): -4 ≤ x ≤ 3