Is this expression a definite negative expression or is it uncertain?

[solid meadow]

a<0<b<c

(c-b)*a

[stone mirage]

@solid meadow what do you think

[solid meadow]

I think its uncertain because lets say we were to give c and b value like: 6-3 the answer would be positive but if we switched the numbers 3-6 it would result in a negative number

so (c-b) could either be negative or positive

[stone mirage]

okay your logic is correct but please read your question again

you are provided with

c>b

[solid meadow]

That is true however the question gave three examples that I didn't include (a+c)*b

the answer for (a+c)*b is indefinite due to not knowing the exact value of a+c

[stone mirage]

okay so have to tell for each case?

[solid meadow]

yes

[stone mirage]

okay so what is the first case

[solid meadow]

I got the answer for the other case however it doesn't seem consistent with the last one (c-b)*a

the first case is (a-b)*c

the second (a+c)*b

the third (c-b)*a

[stone mirage]

okay so starting with the first one

okay so

we know that a is negative and b is positive

what can you conclude about the sign of a-b?

[solid meadow]

it is negative

[stone mirage]

yea

and c?

[solid meadow]

c is positive so if you multiply negative with positive you get negative

[stone mirage]

ys

so 1 completed

now for second part

a is negative and c is postive

now thier addition is intresting

its not necessary that it would give us a postive number

so it would be uncertain

[solid meadow]

that is true

[stone mirage]

yea

and what do you think about the 3rd one

[solid meadow]

the corrct answer for (c-b) is positive but I dont know why it cannot be uncertain like the second one because if we were to give value to (c-b) 1-6= -5 depending on which variable is the largest it could either be negative or positive

[stone mirage]

no

c has to be greater than b

that is given in the question

right?

[solid meadow]

yes thats true

[stone mirage]

so you can't do this

[solid meadow]

but c is also greater than a in the second case

[stone mirage]

yea it does'nt matter tbh

consider 2 numbers

a=-5 and c=3

c is greaater than a and a+c is still negative

[solid meadow]

but if a were -4 and c was 5 it can result in a positive

[stone mirage]

oh yea yea im sorry

okay waait yea that's what i said earlier

[solid meadow]

its ok

[stone mirage]

its uncertain

[solid meadow]

the correct answer for the third one is negative the second one is uncertain and I do not understand why we take into consideration 0<c but not for the second case

[stone mirage]

because in second one

it is

getting added

not mulitplied

[solid meadow]

hm so the third one (c-b) getting subtracted is what makes the difference

[stone mirage]

what do you mean?

[solid meadow]

two positive numbers being subtracted results in a positive number correct?

[stone mirage]

not necessarily

it would be postive if the number that is being subtracted is smaller

like 5-4=1
and 5-6=-1

you see the differnce