Algebra 3ed, page 155,#13

[sowjanyaangara]

Hi
13) if 3c+2d=8,c<-1. which one of the following could be value for d
2.5
3.5
4.5
5.5
6.5
3c+2d=8
2d=8-3c
d=8-3c/2=4-1.5C
d=4-1.5c
d=4-1.5*LT(-1)
d= 4+LT(1.5)
here i am using real numbers to find GT(5.5 )or LT (5.5)
4+LT(1.5) so 4+1=5 or 4 +1.4= 5.4. all these are less than 5.5 .
so it is LT(5.5) instead of GT (5.5). I did not understand the book explanation. Please explain

[tommywallach]

Hey Sowjan,

The mistake you made is that when you multiply or divide an LT by a negative number, you have to flip it into a GT. Remember, you are secretly manipulating an inequality whenever you use LT or GT:

x is less than -2

so x could be -3, -4, -5, etc...but if we multiply both sides by -1:

-x is greater than 2

because x could be 3, 4, 5, etc..

In your example, you needed to switch between here:

d=4-1.5*LT(-1)

and here:

d= 4+LT(1.5)

So this last step should be 4 + GT (1.5).

Another way you could do it is by plugging in using real numbers (which is not what you did, btw).

The biggest that c could be is a little bit less than -1. Let's just use -1:

3(-1) + 2d = 8

-3 + 2d = 8

d = 5.5

Now, let's see what would happen if we plugged in -2 for c:

3(-2) + 2d = 8

-6 + 2d = 8

d = 7

See what happened? As c got smaller, our d actually got bigger. That's how we know it needs to be bigger than 5.5.

Hope that helps!

-t