life is in inequalities

[lowbeam]

I've finished the last part of the Quadratic Equations topics. Time to move on. The next chapter is about linear inequalities. Talk about irony.

well most of it is really what people know in daily lives, in symbols and signs. Lke if x > z, and z>y, then x > y.

Then there is addition / subtraction. if x >y, then x+a>y+a and x-a> y-a, 'a' can be positive, negative or zero.

There is also the multiplication / division. However, whether the extra term is positive or not matters.
e.g. if x>y, 
ax > xy,         x/a > y/a               if a>0,
ax < xy,         x/a < y/a               if a<0

Also, there is the addition of 2 inequalities.
e.g. if x > y, a > b
then x+a > y+b

However, if x+a > y+b
it does not mean x > y and a > b
The relation is in 1 direction only.

And, if x > y, a > b
It does not mean x -a > y - b