Question

Which of the following inequalities are correct please help me ;-;

Answer 1

A is correct

Explanation:

b has a negative value cause it's before 0

but -b will become a positive value thus >0

example:

b is -1

-b = -(-1)

= 1

hope you understand

Answer 2

⇨ Choice A.

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`

Solving Inequality is similar to solving equation. The difference is if the coefficient for the variable is in negative, moving to another side would swap the sign/operator of Inequality.

Thus, our new Inequality would be
`b<0` which is true by the number line itself.

⟺ Choice B

The reason why choice B is not correct because the point a is lesser than the point b. 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<-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<-c\\b>(-c)/(-1)\\b>c`

Also remember that moving a negative coefficient would swap the sign/operator of Inequality.

⇨ Solve for c-term

`-b<-c\\(-b)/(-1)>c\\b>c`

As b>c is not true in the number line. We notice that c point is greater than b point.

Thus, the clear answer is A choice.