which of these expressions always remains negative?

[obsidian urchin]

a<0<b<c

(a-b).c
(a+c).b
(c-b).a

I would appreciate a detailed explanation on how you solve this question

[night hornet]

What does the dot mean?

[obsidian urchin]

dot means multiplication

[night hornet]

Okay. For the future you can use *, that’s the universal symbol for multiplication

[obsidian urchin]

ok understood

[night hornet]

So we can see that these 3 statements consist of two factors. So we multiply two numbers. When is the product of two numbers negative?

[obsidian urchin]

When the numbers are opposite symbols from one another

[night hornet]

Correct

[obsidian urchin]

but what I seem to not understand is b is larger than 0 therefore its positive however in the parenthesis it is treated as a negative number

Is it perhaps a variant?

[night hornet]

You can subtract by a positive number

So if b is positive

And a is negative

What does that make a-b?

[obsidian urchin]

negative

[night hornet]

Correct

And c is positive so what’s can you say about the first expression?

[obsidian urchin]

it is a negative expression

[night hornet]

Yes

Now try to do the same thing for the other two expressions

[obsidian urchin]

a is negative and c is a positive which makes it negative

b is positive we multiply it with negative which is negative

[night hornet]

Not quite

This would be true for multiplication

But it’s addition here

What’s -2+1

And what’s -1+2?

[obsidian urchin]

-1

1

[night hornet]

Yep

So what do we know about the sign of a+c?

[obsidian urchin]

you write down the big numbers symbol correct

[night hornet]

Wdym?

[obsidian urchin]

-2+1

2 is the larger number

[night hornet]

Yes

[obsidian urchin]

so its -1

[night hornet]

That is correct

[obsidian urchin]

ok

[night hornet]

So can you see what that means for a+c?

Not knowing more than what is given to us

[obsidian urchin]

yes we do not know the exact value of a+c

[night hornet]

Correct, it could be larger than 0, smaller than 0 or even equal to 0

So we can’t know whether the second expression is negative

What about the last one?

[obsidian urchin]

its a negative expresssion

about the first expression (a-b) if a were lets say -2 and b were +3 it would result in a positive number

[night hornet]

No, be because -2-(+3) is -2-3=-5

[obsidian urchin]

sorry I used the dot again

its multiplication

[night hornet]

Where?

[obsidian urchin]

nvm I edited it

[obsidian urchin]

ok I understood now

[night hornet]

Question resolved now?

[obsidian urchin]

yes

thank you

[night hornet]

Great

.close