Final answer:
The integer that does not satisfy the inequality x + 2 < 1 when x < 0 is any integer greater than or equal to -1, because the solution to the inequality is x < -1.
Step-by-step explanation:
If x < 0, then we are considering negative numbers for x.
The inequality given is x + 2 < 1.
To find which integer does not satisfy this inequality, we can solve for x by subtracting 2 from both sides, getting x < -1.
This means that any integer greater than or equal to -1 will not satisfy the inequality because the value of x has to be less than -1.
So, integers like 0, 1, 2, and so on will not satisfy this inequality.
Now, if the student has mentioned replacing (0.25 - x) with 0.25 because x is small compared to 0.25, it does not directly apply here, but it suggests we are approximating or simplifying an equation.
This practice usually applies in situations where x is very close to zero, but that information is not necessary for solving the inequality at hand.