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1) -M = |-M| only when M = 0 --> Suff 2) M = 3 or -3 --> Insuff

For statment 1, It's not only M=0 that works. We could try any negative number.
We can pick one example:
o If M = -10, then -M=-(-10) = 10 and |-M| = |-(-10)| = |10| = 10...

1) -M = |-M| only when M = 0 --> Suff 2) M = 3 or -3 --> Insuff

For statment 1, It's not only M=0 that works. We could try any negative number. We can pick one example: o If M = -10, then -M=-(-10) = 10 and |-M| = |-(-10)| = |10| = 10...

So statment 1 alone is not enough

Can someone explain how M can be negative in Statement 1?

1) -M = |-M| only when M = 0 --> Suff 2) M = 3 or -3 --> Insuff

For statment 1, It's not only M=0 that works. We could try any negative number. We can pick one example: o If M = -10, then -M=-(-10) = 10 and |-M| = |-(-10)| = |10| = 10...

So statment 1 alone is not enough

Can someone explain how M can be negative in Statement 1?

I can try

As we have abs ( something ) >= 0, we have:
|-M| >= 0
<=> -M >= 0 as |-M| = -M
<=> M =< 0

1) -M = |-M| only when M = 0 --> Suff 2) M = 3 or -3 --> Insuff

For statment 1, It's not only M=0 that works. We could try any negative number. We can pick one example: o If M = -10, then -M=-(-10) = 10 and |-M| = |-(-10)| = |10| = 10...

So statment 1 alone is not enough

Can someone explain how M can be negative in Statement 1?

I can try

As we have abs ( something ) >= 0, we have: |-M| >= 0 <M>= 0 as |-M| = -M <=> M =< 0

Sorry I am being slow - what I am getting for 1 is -M = |-M| so M = |M| and |M| is never negative... so on that basis I concluded that M has to be positive ... I'm not sure where I have gone wrong?

1) -M = |-M| only when M = 0 --> Suff 2) M = 3 or -3 --> Insuff

For statment 1, It's not only M=0 that works. We could try any negative number. We can pick one example: o If M = -10, then -M=-(-10) = 10 and |-M| = |-(-10)| = |10| = 10...

So statment 1 alone is not enough

Can someone explain how M can be negative in Statement 1?

I can try

As we have abs ( something ) >= 0, we have: |-M| >= 0 <M>= 0 as |-M| = -M <=> M =< 0

Sorry I am being slow - what I am getting for 1 is -M = |-M| so M = |M| and |M| is never negative... so on that basis I concluded that M has to be positive ... I'm not sure where I have gone wrong?

Sorry I am being slow - what I am getting for 1 is -M = |-M| so M = |M| and |M| is never negative... so on that basis I concluded that M has to be positive ... I'm not sure where I have gone wrong?

In bold, it's not correct

We have |M| = |-M|.... but we do not have -M = M

Thanks - so where is the error in my statement below:

Lets take say - M=-3/3 In that case, the Abs is |3|. If -M=|-M| -M=|-3|

If that's the case doesnt -M=-3? or does it equal 3 / -3

Im really lost as to what the rule is here... any chance you could explain in words (in order to help a rather math challeneged lawyer understand the concepts at play?)

Sorry I am being slow - what I am getting for 1 is -M = |-M| so M = |M| and |M| is never negative... so on that basis I concluded that M has to be positive ... I'm not sure where I have gone wrong?

In bold, it's not correct

We have |M| = |-M|.... but we do not have -M = M

Thanks - so where is the error in my statement below:

Lets take say - M=-3/3 In that case, the Abs is |3|. If -M=|-M| -M=|-3|

If that's the case doesnt -M=-3? or does it equal 3 / -3

Im really lost as to what the rule is here... any chance you could explain in words (in order to help a rather math challeneged lawyer understand the concepts at play?)

THANKS!

I will try ... I'm perhaps less expert in pure word explanations

I think u have a mixture in your reasoning between inferences from abs properties and lines of calculation.

First of all, -M = -3 cannot be chosen because M must be negative ... But, I can take this value and demonstrate that it's not working

So, in your example, -M = -3 implies that M = 3. We will consider seperatly the left side of the original equation and then the right one. The objective is to find the same value, indicating that both sides are equal one another.

Sides:
o At left, -M = -3.
o At right, |-M| = |-3| = 3

To conclude on your example, -3 is not equal to 3 implies that M cannot be 3 or -M cannot be -3 and at the same satisfies the equation -M = |-M|

Now, back to the original equation. Luckily, we have 1 property of abs that is very useful : abs (something) >= 0.

By using the original equation, we know now that -M must be positive or equal to 0 to make M a solution to -M = |-M|. M is, by this way, negative or 0.

Another way to see it is to set Z = -M. That means Z = |Z| implies Z positive or 0. Thus, M, the opposite of Z on a number line, is negative or 0.

I will try ... I'm perhaps less expert in pure word explanations

I think u have a mixture in your reasoning between inferences from abs properties and lines of calculation.

First of all, -M = -3 cannot be chosen because M must be negative ... But, I can take this value and demonstrate that it's not working

So, in your example, -M = -3 implies that M = 3. We will consider seperatly the left side of the original equation and then the right one. The objective is to find the same value, indicating that both sides are equal one another.

Sides: o At left, -M = -3. o At right, |-M| = |-3| = 3

To conclude on your example, -3 is not equal to 3 implies that M cannot be 3 or -M cannot be -3 and at the same satisfies the equation -M = |-M|

Now, back to the original equation. Luckily, we have 1 property of abs that is very useful : abs (something) >= 0.

By using the original equation, we know now that -M must be positive or equal to 0 to make M a solution to -M = |-M|. M is, by this way, negative or 0.

Another way to see it is to set Z = -M. That means Z = |Z| implies Z positive or 0. Thus, M, the opposite of Z on a number line, is negative or 0.