Question

Why must you flip the inequality symbol when you divide by a negative number? pls provide two examples too

Answer 1

think about 2<3
well
-2>-3

Answer 2

I don't understand on Why must you flip the inequality symbol when you divide by a negative number?

Answer 3

let's say you had

-x < 2

Answer 4

ok

Answer 5

to solve you could divide both sides by -1 to get

x > -2

OR

you could add x to both sides to get

-x < 2

-x+x < 2 + x

0x < 2 + x

0 < 2 + x

then subtract 2 from both sides to get

0 < 2 + x

0 - 2 < 2 + x - 2

-2 < 0 + x

-2 < x

Answer 6

notice how if we use the second method, we go from -x < 2 to -2 < x

Answer 7

so that's effectively the sign flipping

Answer 8

"sign flipping" is a method, and is not a valid property of algebra :)

if they insist of including it, they should apply it to equalities as well so that you do not have different sets of "rules"

Answer 9

pls explain

Answer 10

lol
I don't think it can be explained any better
now you have to think.

Answer 11

where are you stuck GingaTheNinja?

Answer 12

@amistre64 is it not defined for regular equalities?
or you can easily defined it that way because = would be the same if we "flip" it?

Answer 13

= flips to = so the process is redundant ... but in order to preserve one set of "rules" it should be included as well.

Answer 14

lol so it basically means that when we divide by negative you have to make it equal???

Answer 15

good call:)

Answer 16

what do you mean "have to make it equal"?

Answer 17

like.....

Answer 18

Why must you flip the inequality symbol when you divide by a negative number?

Answer 19

so you have to divide it too.....

Answer 20

12 > 4

divide both sides by -4, does the sign make sense afterwards?

Answer 21

the "reason" is as Jim described ....

Answer 22

"<" is a binary operation on a well ordered set

for convenience, that can be written in a number of different ways

Answer 23

no because -3>-1 is t equal so like I stated before you flip the sign in order to make the situation true

Answer 24

correct, you flip it to retain its "truth" value

Answer 25

ok thanks