Is M not equal to N?

[silvergator]

Is M not equal to N?

1. M+N

2. MN

 

 

 

OA is B

 

 

 

1. M

2. MN

I chose D. Why wrong? on #1??????

[mav]

m + n

 

- both m and n are negative, then m can be either equal or not equal with n.

For ex, m = n = -5 or m = -4, n = -3. Both cases meet m + n

 

- m 0 or vice versa => m and n cannot be equal

For ex: m = -5, n = 4 or m = 2, n = -8

 

since we cannot know whether m = n => 1 is insuf

[silvergator]

Mav,

I subtracted n from both sides of the equation to get m

 

Thanks for any additional information.

[arnabd]

Mav is right - I will go for B

 

Silvergator , in case if inequality subtracting same value many times change the direction of in equality.

[mav]

Mav,

I subtracted n from both sides of the equation to get m

 

I am afraid this approach is wrong. for ex: m = n = -5

we also get m

That's why if we only have m

[silvergator]

So what exactly is the rule then of when I can and when I can't add, subtract, divide or multiply with an inequality?

For instance, if I have m/n>1, can I say that m>n by multiplying both sides by n?

Another example, if I have a-b+c > a+b-c, I can simplify to b>c. So why in this case can I not simplify the term????????

 

Thanks

[mav]

So what exactly is the rule then of when I can and when I can't add, subtract, divide or multiply with an inequality?

For instance, if I have m/n>1, can I say that m>n by multiplying both sides by n?

Another example, if I have a-b+c > a+b-c, I can simplify to b>c. So why in this case can I not simplify the term?

 

Thanks

 

Silver,

 

I think you are more familiar with equation, rite. We all know that in equation we can subtract, add to both sides of the equation freely. Also we can multiply, divide both side with the same number/expression (provided it is not zero).

 

In inequality, it is similar when we add, subtract smth to/from both sides, the inequality is still valid. In your example, we can netoff a

 

a - b + c > a + b -c -b + c > b - c (subtract a from both side) -2b > -2c b

 

you have to be very careful with positive and negative sign when dealing with equation and inequality. Whenever a number/expression is moved from one side to the other, it's negative/positive sign will be changed to the other. For ex: m > n m - n > 0

 

In inequality, if we multiply/divide two sides with positive number, we get new inequality with same direction:

 

a > b (if c > 0) ac > bc

and if we have ac > bc (if c > 0) we can get a > b (divide two sides by c)

 

If we multiply/divide two sides with negative number, we get new inequality with opposite direction:

 

a > b (if c ac

ac > bc (c a

 

Thus, in your example: m/n > 1 we cannot multiply two side with n to get m > n since we do not know n is positive or negative, so we have two circumstances:

n > 0: m/n > 1 (m/n)*n > 1*n m > n (your approach)

n 1 (m/n)*n m

 

HTH