# Maths inequalities help please!

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Hi guys,

So for this question I did:

-2x^2 +x +3≥ 0

2x^2 -x-3≤ 0

(2x-3)(x+1)≤ 0

Then I got stuck on drawing the graph.

This is what is shown in the mark scheme:

Attachment 738542738548

However why can't the graph be:

Attachment 738542738548738600

So for this question I did:

-2x^2 +x +3≥ 0

2x^2 -x-3≤ 0

(2x-3)(x+1)≤ 0

Then I got stuck on drawing the graph.

This is what is shown in the mark scheme:

Attachment 738542738548

However why can't the graph be:

Attachment 738542738548738600

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#2

(Original post by

Hi guys,

So for this question I did:

-2x^2 +x +3≥ 0

2x^2 -x-3≤ 0

(2x-3)(x+1)≤ 0

Then I got stuck on drawing the graph.

This is what is shown in the mark scheme:

However why can't the graph be:

**sienna2266**)Hi guys,

So for this question I did:

-2x^2 +x +3≥ 0

2x^2 -x-3≤ 0

(2x-3)(x+1)≤ 0

Then I got stuck on drawing the graph.

This is what is shown in the mark scheme:

However why can't the graph be:

Not like it matters anyway, it's all just for the purposes of working out the same region.

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#3

(Original post by

Hi guys,

So for this question I did:

-2x^2 +x +3≥ 0

2x^2 -x-3≤ 0

(2x-3)(x+1)≤ 0

Then I got stuck on drawing the graph.

This is what is shown in the mark scheme:

Attachment 738542738548

However why can't the graph be:

Attachment 738542738548738600

**sienna2266**)Hi guys,

So for this question I did:

-2x^2 +x +3≥ 0

2x^2 -x-3≤ 0

(2x-3)(x+1)≤ 0

Then I got stuck on drawing the graph.

This is what is shown in the mark scheme:

Attachment 738542738548

However why can't the graph be:

Attachment 738542738548738600

in the lower graph you are looking for values of x where the curve lies below ( or on ) the x axis

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#4

(Original post by

both graphs are fine... in the top graph you are looking for values of x where the curve lies above ( or on ) the x axis

in the lower graph you are looking for values of x where the curve lies below ( or on ) the x axis

**the bear**)both graphs are fine... in the top graph you are looking for values of x where the curve lies above ( or on ) the x axis

in the lower graph you are looking for values of x where the curve lies below ( or on ) the x axis

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#5

(Original post by

I would disagree, the equation given in the question is a negative quadratic and therefore the graph you sketch should portray this.

**u12davisd**)I would disagree, the equation given in the question is a negative quadratic and therefore the graph you sketch should portray this.

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#6

**u12davisd**)

I would disagree, the equation given in the question is a negative quadratic and therefore the graph you sketch should portray this.

It doesn't specify you have to draw a specific quadratic graph- "use a sketch of appropriate quadratic graphs..."

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#7

**sienna2266**)

Hi guys,

So for this question I did:

-2x^2 +x +3≥ 0

2x^2 -x-3≤ 0

(2x-3)(x+1)≤ 0

Then I got stuck on drawing the graph.

This is what is shown in the mark scheme:

Attachment 738542738548

However why can't the graph be:

Attachment 738542738548738600

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#8

(Original post by

But you don't have to draw the negative quadratic graph. The OP has clearly taken all terms on the other side of the inequality and correctly drawn the corresponding graph. The problem can be solved either way...

It doesn't specify you have to draw a specific quadratic graph- "use a sketch of appropriate quadratic graphs..."

**Anonymouspsych**)But you don't have to draw the negative quadratic graph. The OP has clearly taken all terms on the other side of the inequality and correctly drawn the corresponding graph. The problem can be solved either way...

It doesn't specify you have to draw a specific quadratic graph- "use a sketch of appropriate quadratic graphs..."

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(Original post by

Well it can't be like that because it's the reflected graph from the one asked by the question! They're not the same, they only share the same roots.

Not like it matters anyway, it's all just for the purposes of working out the same region.

**RDKGames**)Well it can't be like that because it's the reflected graph from the one asked by the question! They're not the same, they only share the same roots.

Not like it matters anyway, it's all just for the purposes of working out the same region.

For this particular question(in the link above):

We or I came to the conclusion that the graph can be sketched in 2 ways:

First way:

Attachment 738556738558

However, now coming back to this, I think the second graph is wrong because I did x^2 +8<2x^2 +x +6 --> -x^2 -x +2<0 --> x^2 +x -2>0 --> (x-1)(x+2)>0

Clearly, the graph has a maximum point as it is -x^2 -x +2<0.

Could you please let me know your thoughts?

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Hey guys, thanks for your replies!

Here is a very similar question which is rather confusing:

I've outlined my confusion in my reply to RDKGames.. Could someone please help with this one too?

So basically I understand they're asking you to "sketch" to just find out the solutions to the question but what I am specifically wondering about is the correct sketch of the graph. This one above is rather confusing

Please check my post above if possible- it would be much appreciated

Here is a very similar question which is rather confusing:

I've outlined my confusion in my reply to RDKGames.. Could someone please help with this one too?

So basically I understand they're asking you to "sketch" to just find out the solutions to the question but what I am specifically wondering about is the correct sketch of the graph. This one above is rather confusing

Please check my post above if possible- it would be much appreciated

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#11

(Original post by

Hey guys, thanks for your replies!

Here is a very similar question which is rather confusing:

I've outlined my confusion in my reply to RDKGames.. Could someone please help with this one too?

So basically I understand they're asking you to "sketch" to just find out the solutions to the question but what I am specifically wondering about is the correct sketch of the graph. This one above is rather confusing

Please check my post above if possible- it would be much appreciated

**sienna2266**)Hey guys, thanks for your replies!

Here is a very similar question which is rather confusing:

I've outlined my confusion in my reply to RDKGames.. Could someone please help with this one too?

So basically I understand they're asking you to "sketch" to just find out the solutions to the question but what I am specifically wondering about is the correct sketch of the graph. This one above is rather confusing

Please check my post above if possible- it would be much appreciated

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(Original post by

If the coefficient of x in x^2 is positive it will form a u-shaped graph and if it's negative it will form an n-shaped graph.

**dont know it**)If the coefficient of x in x^2 is positive it will form a u-shaped graph and if it's negative it will form an n-shaped graph.

It has to be the other way round? - so like n shaped?

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#13

(Original post by

Thanks but I am specifically talking about there being one graph on the axis not the one in the mark scheme. So this is not correct right:

It has to be the other way round? - so like n shaped?

**sienna2266**)Thanks but I am specifically talking about there being one graph on the axis not the one in the mark scheme. So this is not correct right:

It has to be the other way round? - so like n shaped?

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#14

(Original post by

No that is correct. By rearranging you get x^2+x-2>0. Since the coefficient of x is positive, you get a U-shape, so that's right.

**dont know it**)No that is correct. By rearranging you get x^2+x-2>0. Since the coefficient of x is positive, you get a U-shape, so that's right.

**-x^2 -x +2<0**--> x^2 +x -2>0 --> (x-1)(x+2)>0

Clearly, the graph has a maximum point as it is -x^2 -x +2<0. "

Just copy and pasted what OP did. I don't think the graph is correct cos this is the graph

**-x^2 -x +2<0 .**The negative in front x^2 means it's got a maximum as opposed to a minimum point. The one OP has drawn is x^2 +x -2>0 and so the graph has been reflected which is wrong I think.

But that's just my gut instinct -hopefully some of the others will confirm

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#15

(Original post by

" x^2 +8<2x^2 +x +6 -->

Clearly, the graph has a maximum point as it is -x^2 -x +2<0. "

Just copy and pasted what OP did. I don't think the graph is correct cos this is the graph

But that's just my gut instinct -hopefully some of the others will confirm

**h26**)" x^2 +8<2x^2 +x +6 -->

**-x^2 -x +2<0**--> x^2 +x -2>0 --> (x-1)(x+2)>0Clearly, the graph has a maximum point as it is -x^2 -x +2<0. "

Just copy and pasted what OP did. I don't think the graph is correct cos this is the graph

**-x^2 -x +2<0 .**The negative in front x^2 means it's got a maximum as opposed to a minimum point. The one OP has drawn is x^2 +x -2>0 and so the graph has been reflected which is wrong I think.But that's just my gut instinct -hopefully some of the others will confirm

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**RDKGames**)

Well it can't be like that because it's the reflected graph from the one asked by the question! They're not the same, they only share the same roots.

Not like it matters anyway, it's all just for the purposes of working out the same region.

Ahh thanks so much for replying So I see what you mean there. Just to make sense of this. Here is the thread for a similar question that you helped me with ages ago: https://www.thestudentroom.co.uk/sho...5154306&page=2

For this particular question(in the link above):

We or I came to the conclusion that the graph can be sketched in 2 ways:

First way:

Second way:

Attachment 738574

However, now coming back to this, I think the second graph is wrong because I did x^2 +8<2x^2 +x +6 --> -x^2 -x +2<0 --> x^2 +x -2>0 --> (x-1)(x+2)>0

Clearly, the graph has a maximum point as it is -x^2 -x +2<0.

Could you please let me know your thoughts?

I just felt I needed to refer back to this one as it contradicts the question in this thread

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#17

(Original post by

It would be extremely appreciated if you could please kindly reply back as you explain things so well.

Ahh thanks so much for replying So I see what you mean there. Just to make sense of this. Here is the thread for a similar question that you helped me with ages ago: https://www.thestudentroom.co.uk/sho...5154306&page=2

For this particular question(in the link above):

We or I came to the conclusion that the graph can be sketched in 2 ways:

First way:

However, now coming back to this, I think the second graph is wrong because I did x^2 +8<2x^2 +x +6 --> -x^2 -x +2<0 --> x^2 +x -2>0 --> (x-1)(x+2)>0

Clearly, the graph has a maximum point as it is -x^2 -x +2<0.

Could you please let me know your thoughts?

I just felt I needed to refer back to this one as it contradicts the question in this thread

**sienna2266**)It would be extremely appreciated if you could please kindly reply back as you explain things so well.

Ahh thanks so much for replying So I see what you mean there. Just to make sense of this. Here is the thread for a similar question that you helped me with ages ago: https://www.thestudentroom.co.uk/sho...5154306&page=2

For this particular question(in the link above):

We or I came to the conclusion that the graph can be sketched in 2 ways:

First way:

However, now coming back to this, I think the second graph is wrong because I did x^2 +8<2x^2 +x +6 --> -x^2 -x +2<0 --> x^2 +x -2>0 --> (x-1)(x+2)>0

Clearly, the graph has a maximum point as it is -x^2 -x +2<0.

Could you please let me know your thoughts?

I just felt I needed to refer back to this one as it contradicts the question in this thread

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(Original post by

It's not *wrong* it's just different graphs representing the same solutions to the inequality. If you want to sketch what the question lays out then yes you need to strictly follow the first way, but generally it doesn't matter.

**RDKGames**)It's not *wrong* it's just different graphs representing the same solutions to the inequality. If you want to sketch what the question lays out then yes you need to strictly follow the first way, but generally it doesn't matter.

This is what I mean by upside down U shaped: and this is caused by -x^2 -x +2<0 -the solutions would be x<-2 or x>1

This is what I mean by U shaped graph: and this is caused by x^2 +x -2>0 - the solutions would be be x<-2 or x>1

Attachment 738576738578

Both these graphs are from x^2 +8<2x^2 +x +6 and these graphs are not from the mark scheme -just an alternative graph i think could work

So I understand both these graphs yield the same solutions and they are both correct to use to work out the solutions. But what I am specifically asking is which one would be the correct representation/sketch of the graph x^2 +8<2x^2 +x +6?

Would be really really appreciated if you could please reply back. Thank you so much!

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#19

(Original post by

But what I am specifically asking is which one would be the correct representation/sketch of the graph x^2 +8<2x^2 +x +6?

Would be really really appreciated if you could please reply back. Thank you so much!

**sienna2266**)But what I am specifically asking is which one would be the correct representation/sketch of the graph x^2 +8<2x^2 +x +6?

Would be really really appreciated if you could please reply back. Thank you so much!

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(Original post by

Neither or both, whichever way you want to think about it. But the point is that one does not take precedence over the other, they are both equally as fine in order to answer the original inequality and both are fine to sketch in order to answer it.

**RDKGames**)Neither or both, whichever way you want to think about it. But the point is that one does not take precedence over the other, they are both equally as fine in order to answer the original inequality and both are fine to sketch in order to answer it.

So for this question I did:

-2x^2 +x +3≥ 0

2x^2 -x-3≤ 0

(2x-3)(x+1)≤ 0

Then I got stuck on drawing the graph.

This is what is shown in the mark scheme:

However why can't the graph be:

Attachment 738584738586

**RDKGames**)

Well it can't be like that because it's the reflected graph from the one asked by the question! They're not the same, they only share the same roots.

Not like it matters anyway, it's all just for the purposes of working out the same region.

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