I'm confused. Why is the answer to l9/10+5xl

Question

I'm confused. Why is the answer to l9/10+5xl<11/10, -2/5<x<1/25?
I thought the signs flip when you divide.

turingtest · Answer

do you mean$$\left| (9/10)+5x \right|<11/10$$
or is it$$\left| 9/(10+5x) \right|<11/10$$

anonymous · Answer

The first one

anonymous · Answer

Sorry I used capital i's for the absolute value

phi · Answer

If you need more info, watch Khan's video, (and the following one) http://www.khanacademy.org/video/absolute-value-inequalities-example-1?playlist=Algebra+I+Worked+Examples

turingtest · Answer

-11/10<9/10+5x<11/10
subtract 9/10:
-20/10<5x<2/10
-2<5x<1/5
divide by 5:
-2/5<x<1/25

Since we only divided by 5 the direction of the signs did not change. Had we had to take a reciprocal, they would have.

 Consider 
1/x<1/3
take the reciprocal:
x>3
and the signs change. 

We can see this by
multiplying both sides of 
1/x<1/3
by 3x WITHOUT changing the sign:
3<x

anonymous · Answer

I'm soooo confused but thanks.