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Inequalities and descriminant- c1

Slightly confused as to when I do this no1 or no2.

I actually don't need how to explain this. How are you supposed to know whether to write the equation as when x is between two numbers (Like in no1) or X is greater than/less to each number as is No2.

For no. 2 I mean X is less than -3.

Also, in No1 why is X less than 1 and not less than or equal to. I'm confused at to why the inequality changes.

(edited 8 years ago)

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Reply 1

Zacken

Original post by Questioness

By looking at the graph. If the shaded portion is in between two values then you put x as inbeween two values. As you have for Q1, for Q2 the shaded region is all the right of 2 and all the left of -3.

Reply 2

abitpissy

Original post by Zacken

Only the equation is the given. I drew the graph because I know what to do I just understand when to do it or why.

Reply 3

Andy98

Original post by Questioness

Slightly confused as to when I do this no1 or no2.

Well, you shouldn't have got a quadratic for number one; remember if the fraction is equal to zero, the numerator must be.

For number two you have the right idea, draw the graph and see where the y values are above 0

Reply 4

Andy98

Original post by Zacken

I'm a slow typist; but I'm surprised you didn't notice the mistake in Q1 :wink:

Reply 5

Zacken

Original post by Andy98

Well, you shouldn't have got a quadratic for number one; remember if the fraction is equal to zero, the numerator must be.

Huh? Look at it again.

Reply 6

Zacken

Original post by Andy98

I'm a slow typist; but I'm surprised you didn't notice the mistake in Q1 :wink:

Because there isn't one.

Reply 7

Zacken

Original post by Questioness

Only the equation is the given. I drew the graph because I know what to do I just understand when to do it or why.

You're meant to sketch the graph each time.

Reply 8

balanced

saw the title, thought it was politics. Mb lol.

Reply 9

Zacken

Original post by Questioness

Also, in No1 why is X less than 1 and not less than or equal to. I'm confused at to why the inequality changes.

x=1

then you end up with a division by 0.

Reply 10

Andy98

Original post by Zacken

Huh? Look at it again.

Original post by Zacken

Because there isn't one.

Well where does the quadratic come from?

Here is what I would do:

\frac{x-4}{x-1}<0

implies

x-4<0

, thus

x<4

Reply 11

Zacken

Original post by Andy98

Well where does the quadratic come from?

Here is what I would do:

\frac{x-4}{x-1}<0

implies

x-4<0

, thus

x<4

Classic error. What if

x = -10

\frac{-10 - 4}{-10 - 1} = \frac{-14}{-11} = \frac{14}{11} > 0

Yet

-10 < 4

What you've done is you've multiplied both sides of the inequality by

x-1

which might be negative so that's invalid.

What the OP has done is multiplied both side by

(x-1)^2

by which is always positive.

Reply 12

abitpissy

Original post by Zacken

And how will I know where to shade? If I don't know if the equation is 'in between' or not.

Reply 13

Zacken

Original post by Questioness

And how will I know where to shade? If I don't know if the equation is 'in between' or not.

When your inequality is quadratic > 0: Look at your curve and see where the curve is above or below the x-axis. Shade the regions for which the curve is above the x-axis.

When your inequality is quadratic < 0: Look at your curve and see where the curve is above or below the x-axis. Shade the regions for which the curve is below the x-axis.