Question

When to switch the less-than, greater-than, equal to sign in an inequality

Answer 1

when the greater variable is in negative sign

Answer 2

-x < 2
will be turned into,
x > -2

Answer 3

when you divide by a negative number the sign flips

Answer 4

Sorry i currently have no answer for WHY. :(

Answer 5

Well, okay then. Thanks though.

Answer 6

The answer for why becomes pretty clear when you think about it as a number line. Picture -x < 2 on the number line. That means that -x can be 1, 0, -1, -2, -3... which means that x can be -1, 0, 1, 2, 3... which means x > -2.

Answer 7

That's just an intuitive way of thinking about it. For a formal reason as to why you'll want to look at the definition of the ordering structure and the trichotomy law.