# Inequality: If a > b, and if c > d, then....

#### NSH

##### New member
help with solving this problem

If a>b, and if c>d, then.................

#### Subhotosh Khan

##### Super Moderator
Staff member
Re: INEQUALITY

NSH said:
help with solving this problem

If a>b, and if c>d, then.................
That is not a "proper" question - what else is provided here?

#### stapel

##### Super Moderator
Staff member
NSH said:
If a>b, and if c>d, then....
There are any number of "conclusions" one could draw from the above. Without parameters, there is, unfortunately, no possible way of knowing which one particular conclusion is expected for this exercise. Sorry!

Eliz.

#### Loren

##### Senior Member
If a>b, and if c>d, then....

If 10>9, and if 6>5, then....you might conclude that 10>5, but...
If 10>9, and if 15>14, then....can you say that 10>14?

If 10>9, and if 6>5, then.... could say that 10+6 > 9+5 or 10-6 > 9-5 or 10*6 > 9*5 or 10/6 > 9/5 ??? One or more of these is not true. One or more are true.

I imagine you are to draw conclusions similar to these, only using a, b, c and d. In other words...
If a>b, and if c>d, then....is a+c always greater than b+d? What if a, b, c, and d are negative numbers?

#### soroban

##### Elite Member
Hello, NSH!

$$\displaystyle \text{If }a>b\text{ and }c>d\text{, then } \hdots$$

$$\displaystyle \text{If we are concerned with the four arithmetic operations,}$$
. . $$\displaystyle \text{only }addition\text{ is "dependable."}$$

$$\displaystyle \text{We can safely conclude that: }\;\boxed{\:a + c \:> \:b + d\:}$$

$$\displaystyle \text{The others: }\begin{Bmatrix} a-c & >& b-d \\ ac & > &bd \\ \frac{a}{c} & > & \frac{b}{d}\end{Bmatrix}\;\;\text{may or may not be true.}$$

#### NSH

##### New member
Re: INEQUALITY

Subhotosh Khan said:
NSH said:
help with solving this problem

If a>b, and if c>d, then.................
That is not a "proper" question - what else is provided here?
This is the only thing that was provided.

#### NSH

##### New member
Re:

stapel said:
NSH said:
If a>b, and if c>d, then....
There are any number of "conclusions" one could draw from the above. Without parameters, there is, unfortunately, no possible way of knowing which one particular conclusion is expected for this exercise. Sorry!

Eliz.
Thanks.

#### Subhotosh Khan

##### Super Moderator
Staff member
Re: INEQUALITY

NSH said:
quote="NSH"]help with solving this problem

If a>b, and if c>d, then.................

This is the only thing that was provided.[/quote]

Then answer is "it cannot be determined".