# Solving InequalitiesWatch

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#1
Here is my working out

However in the book the sign is the other way round which I know is correct but why are they flipping the sign?
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7 years ago
#2
Because you have divided by a negative number
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7 years ago
#3
Consider this

10 > 7

Multiply/Divide both by -1 and you get -10 and -7

I assume that you are happy that

-10 < -7
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#4
(Original post by TenOfThem)
Because you have divided by a negative number
Is there any proof around it or is it something that I'll just have to learn.
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7 years ago
#5
(Original post by zed963)
Is there any proof around it or is it something that I'll just have to learn.
there probably is a formal proof but its so trivial you might as well learn it
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7 years ago
#6
Whenever you divide by a negative number, you flip the inequality sign! Just learn that and you'll be fine
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7 years ago
#7
(Original post by zed963)
Is there any proof around it or is it something that I'll just have to learn.
proof?

was post 3 not enough "proof"

It is a fact .... it is how negative numbers operate
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#8
Here's my working out

anyone know what I'm doing wrong

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7 years ago
#9
(Original post by zed963)
Here's my working out

anyone know what I'm doing wrong

where did the 1 go?
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7 years ago
#10
(Original post by zed963)
Here's my working out

anyone know what I'm doing wrong

There's an error in line 1-> line 2. Might be more, I didn't look.
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#11
(Original post by Slumpy)
There's an error in line 1-> line 2. Might be more, I didn't look.
I times the whole thing by 2, I don't see what's wrong with it.
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7 years ago
#12
(Original post by zed963)
I times the whole thing by 2, I don't see what's wrong with it.
I repeat

Where did the 1 go?
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#13
(Original post by TenOfThem)
I repeat

Where did the 1 go?
OOH I just did something stupid.

Come to think of it I don't even know why I did it.
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#14
Here's the correct version

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7 years ago
#15
(Original post by zed963)
OOH I just did something stupid.

Come to think of it I don't even know why I did it.
Given that this seems to be common response this afternoon ... perhaps you need to check your work first before posting
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#16
(Original post by TenOfThem)
Given that this seems to be common response this afternoon ... perhaps you need to check your work first before posting
It's been a long day lol
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7 years ago
#17
(Original post by zed963)
Is there any proof around it or is it something that I'll just have to learn.
In simple terms, when you work with inequalities you apply a simple function to both sides. If the function is increasing, the inequality remains the same, if the function is decreasing, the sign flips.

Now of course you don't need to think of this every time you work through an inequality, but it helps to understand why the sign sometimes changes and serves as a sort of 'proof' if you will.

In your case, multiplying by -1 is equivalent to taking of both sides where As you well know decreases, hence the change of sign.
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7 years ago
#18
(Original post by zed963)
Here's the correct version

yeah that's right, what's wrong?
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7 years ago
#19
For multiplying/dividing by a negative number, visualise the inequalities change on a number line
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#20
So for this questions what happens to the signs

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