is d negative

[rustom.hakimiyan]

Question 2:

If I don't flip statement number two, can I still add or subtract it?

Use a common-sense analogy again.

"- I want to buy an item that costs $50. (x = 50)
- I have a discount coupon worth less than $10. (y < 10)
- Therefore, when I take the discount (= subtract), the resulting price will be more than $40. (x - y > 40)

So, "=" minus "<" is actually ">".

EXTREMELY clear. Thanks a ton.

Let me test my knowledge at a random scenario -- am I on the right track?

Situation 1:
If bought a shoe for $50 (x=50)
My friend bought a shoe that is less than $100 (y<100)
The total amount will be less than 150 = x+y<150. Correct?

So to summarize this rule: Sum of equal and less than is less than. Correct?


Situation 2:
I paid someone $50(x=-50)
My friend was paid more than $10(y>10)
The total loss that we both will end up sharing is x+y<-40

So to summarize this rule: Sum of equal(although negative) and greater than will be less than. In this case, negative matters unlike your statement above. Is this correct?

You're absolutely right -- memorizing these so called rules seem rather ridiculous. But, solving this within two minutes without the rules would be rather challenging.

[RonPurewal]

Situation 1:
If bought a shoe for $50 (x=50)
My friend bought a shoe that is less than $100 (y<100)
The total amount will be less than 150 = x+y<150. Correct?

So to summarize this rule: Sum of equal and less than is less than. Correct?

Yes.

Situation 2:
I paid someone $50(x=-50)
My friend was paid more than $10(y>10)
The total loss that we both will end up sharing is x+y<-40

So to summarize this rule: Sum of equal(although negative) and greater than will be less than. In this case, negative matters unlike your statement above. Is this correct?

No.
Addition and subtraction are NEVER affected by the +/- signs of the numbers you're adding.

The issue is that negative numbers are a bit screwy when it comes to intuition.
Specifically, "you lose less than $40" is actually "outcome > -40". Remember, a smaller negative number is greater than a bigger negative number.
If this is still too abstract to really click, then just put some numbers in there. E.g., if you lose $30, then that's a profit of -30, and -30 > -40.