1. ## Inequalities

Hi There,

Just something i wanted to clarify.

I have the equation:

a * b <= b

1)

a >= b/b
a>=1
a > 0

or

2)

a <= b/b
a <= 1
a < 2

Its just that in answer one i cant remember if you flip the inequality sign because you are bringing the b over to the other side and dividing.

2. It's the second one. You only switch the sign if you divide by a negative number.

Bo

Although I'm not sure why you'd finish it with <2. Can you not just leave your answer as a<=1

3. 1*5=<5 so 1=<1
2*(-5)=<-5 so 2=<1 which is not true.
So if you divide by a negative number then switch the sign (and don't divide by 0). So the thing is depending on b. If you don't know anything about it then you should do the cases b>0, b<0 and b=0 separately.
So the solution to the inequality $a\cdot b\le b$ is $b<0\quad a\ge 1$ and $b>0\quad a\le 1$ and $b=0\quad \forall a\in\mathbb{R}$.