Question

Why does the inequality sign have to be flipped when multiplying and dividing by a negative number like in -2x>10?

PLZ HELP

Answer 1

help? @Loser66

Answer 2

ok

Answer 3

yes.

Answer 4

I think you flip the sign because the value changes to negative.....I just do the rule of flipping it. Never really thought about the explanation

Answer 5

here is one explanation
it relies on defining \(a<b\) and there is a positive \(p\) with \(a+p=b\)

Answer 6

for example \(-2<1\) because \(-2+3=1\)

Answer 7

now multiply by a negative number call it \(n\)
\[n(a+p)=nb\\
na+np =nb\]

Answer 8

now since \(p\) is positive and \(n\) is negative that means \(np\) is negative

Answer 9

im sorry im just confused

Answer 10

:( me too.

Answer 11

so the inequality has been switched as now
\[na=nb-np\] and \(np>0\)

Answer 12

if you want a satisfactory explanation of why you change the sense of the inequality, you need an actual definition for what \(a<b\) means

Answer 13

an example may make it clear
we say \(-2<1\) because \(-2+3=1\) and \(3>0\)

Answer 14

-2x>10 this is hte example i was given in the question

Answer 15

now multiply
\[-2+3=1\] on both sides by a number, i pick \(-5\)

Answer 16

you get
\[10-15=-5\] or
\[10=-5+15\] making \(10>-5\) and the inequality has been switched

Answer 17

do you get it? @Loser66

Answer 18

How to say!! Have to confess that I got until a<b meaning.

Answer 19

i dont even know at this point what to put lol

Answer 20

ok, I got what he meant now. Wow!!

Answer 21

hahaha... it's fun when I don't know how to explain but I have to explain the explanation of other.

Answer 22

haha

Answer 23

@arianaharmony Your question is about "Why we have to change the sign when multiple/ divide both sides of an inequality with a negative number?" right?
It's not "solve -2x>10" right?
So that, let the original problem aside. just answer your question, ok??

Answer 24

right

Answer 25

It's only flipped when you divide by a negative

Answer 26

he gave us an example -2<1 and definition of it, it says " minus two is called lesser than one when there is a number such that minus two plus that number equal to one" got this part?

Answer 27

not really..

Answer 28

oh ok i think i might get it

Answer 29

In real life: Loser is poor, all his property is 5 dollars
arianaharmony is rich, he has 8 dollars
so that Loser's money is < arianaharmony 's money. Why I can say so?? Yes I can say that because Loser's money + some more = arianaharmony's money
Proof 5 + 3 =8

Answer 30

so that "some more" is 3, got me?

Answer 31

ya ok i get that

Answer 32

hahaha... let big one do big thing, small one do small thing, I am happy to be small one to be here to explain this stuff to you. lol

Answer 33

now, back to his example, so -2<1 when -2+ "some more" =1, that "some more" is 3 , OK?
-2+3=1

Answer 34

yes okay.
but after this question would you mind helping me with 2 other questions?
ik its alot but i need help lol sorry

Answer 35

Actually, if you can understand the stuff, it's perfect. but if you don't, memorize the rule is perfect, too. hihihi...
Now, what are your problems?

Answer 36

wait. what was the answer to this question exactly?

Answer 37

WAAAT?? ok
-2x>10 divided both sides by -2 and change the sign, you have x<5

Answer 38

but the question is
Why does the inequality sign have to be flipped when multiplying and dividing by a negative number

Answer 39

if you dont know its okay. can you help me with my other questions tho plz @Loser66

Answer 40

I give you the link to get a neat answer, hahaha.... click at the question you want to know the answer. The Answerer is a Ph.D http://mathforum.org/library/drmath/sets/select/dm_inequal_neg.html

Answer 41

lalalala.....lallala. life is beautiful. hahaha

Answer 42

can you help me with this problem?
Explain the steps in solving the following absolute value equation. 2|x-2|=12.

Answer 43

close the post, open a new one to get help. I told you, I don't know how to explain. I am sorry for that.

Answer 44

ok thanks