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Quadratic Inequality

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.

Reply 1

Smug Life

-4 < x < 1/2

What other way would you put it?

Reply 2

username1500433

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

Reply 3

Smug Life

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?

(edited 8 years ago)

Reply 4

bartbarrow

Here's what we were taught. Please excuse the handwriting!

Reply 5

Muttley79

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.

Reply 6

Guills on wheels

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?

Reply 7

davros

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.

Reply 8

Slenderman

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.