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1. Here is my working so far:

(2x-1)(x+4)<0

2x-1<0
2x<1
x<1/2

x+4<0
x<-4

How do I then know which sign to flip for the answer? I don't understand. Thanks.
2. -4 < x < 1/2

What other way would you put it?
3. (Original post by Smug Life)
-4 < x < 1/2

What other way would you put it?
Why is it that though and not: x<-4 and x>1/2
4. (Original post by will_jg)
Why is it that though and not: x<-4 and x>1/2
Have you tried to draw a parabola for that? It doesn't make sense. How could something be greater than 1/2 and less than -4 at the same time?
5. Here's what we were taught. Please excuse the handwriting!

6. (Original post by will_jg)
Here is my working so far:

(2x-1)(x+4)<0

2x-1<0
2x<1
x<1/2

x+4<0
x<-4

How do I then know which sign to flip for the answer? I don't understand. Thanks.
I always suggest sketching the curve so you can 'see' it.
7. (Original post by will_jg)
Here is my working so far:

(2x-1)(x+4)<0

2x-1<0
2x<1
x<1/2

x+4<0
x<-4

How do I then know which sign to flip for the answer? I don't understand. Thanks.
surely just plugging x=5 should tell you?
8. (Original post by will_jg)
Here is my working so far:

(2x-1)(x+4)<0

2x-1<0
2x<1
x<1/2

x+4<0
x<-4

How do I then know which sign to flip for the answer? I don't understand. Thanks.
You can't just work with each bracket in isolation! If one bracket is negative then the other one has to be positive, and vice versa. So you'll get 2 conditions to combine for each possibility.
9. Sketch the curve ALWAYS. Never ever don't do it.

From the inequality you see (2x-1)(x+4)<0

<0 meaning below the axis so you want the solutions below the axis. That's why you get what they said above.
10. I get it now thanks everybody!

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