Which of the following values of 𝑥 does not satisfy the inequality 𝑥 is greater than negative nine? (A) Negative two, (B) negative four, (C) negative eight, or (D) negative nine.
One way to think about this would be to draw 𝑥 is greater than negative nine on a number line. If we start with zero and then add negative nine, to show that 𝑥 is greater than negative nine, we would draw a circle around that point, but we would not fill it in. This is because 𝑥 is not equal to negative nine; it must be greater than negative nine. From there, we can draw an arrow extending to the right because everything to the right of negative nine on the number line is greater than negative nine.
If we wanted to consider the four places that we were given — negative two, negative four, negative eight, and negative nine — we can see that negative eight, negative four, and negative two are all solutions to the inequality 𝑥 is greater than negative nine. However, because this inequality says greater than and it does not say greater than or equal to, negative nine cannot satisfy this inequality. And therefore, from this list, the only value of 𝑥 that does not satisfy the inequality is (D), negative nine.