Answer:
⇨ Choice A.
Step-by-step explanation:
We'll consider three choices and compare the answers with the given number line and points.
⟺ Choice A
This is the correct answer and here is why.
![-b>0](https://tex.z-dn.net/?f=-b%3E0)
Solving Inequality is similar to solving equation. The difference is <u>if the coefficient for the variable is in negative, moving to another side would swap the sign/operator of Inequality.</u>
Thus, our new Inequality would be
which is true by the number line itself.
⟺ Choice B
The reason why choice B is not correct because <u>the point a is lesser than the point b</u>. It's obvious that point a cannot be greater than point b.
⟺ Choice C
The reason why choice C is not correct because if we solve the Inequality.
![-b](https://tex.z-dn.net/?f=-b%3C-c)
We can either solve for b-term or c-term, the outcome would be the same. I'll solve for both terms.
⇨ Solve for b-term
![-b\frac{-c}{-1}\\b>c](https://tex.z-dn.net/?f=-b%3C-c%5C%5Cb%3E%5Cfrac%7B-c%7D%7B-1%7D%5C%5Cb%3Ec)
Also remember that <u>moving a negative coefficient would swap the sign/operator of Inequality.</u>
⇨ Solve for c-term
![-bc\\b>c](https://tex.z-dn.net/?f=-b%3C-c%5C%5C%5Cfrac%7B-b%7D%7B-1%7D%3Ec%5C%5Cb%3Ec)
As b>c is not true in the number line. We notice that <u>c point is greater than b point</u>.
Thus, the clear answer is A choice.