AQA C1 Inequalities question

I really need help with these inequalities questions i've tried everything and i don't know how to get the answers they are really hard for me to do.

a) x^2+x-6 =< 0
b) x^2-3x-28 => 0
c) 25-x^2 > 0

Thanks

Reply 1

Chlorophile

Original post by Sayless

Solve the inequalities as ordinary equations and using the solutions, sketch the graphs. You should then be able to work out the inequalities for x by looking at which parts of the graph are less than or greater than 0.

Reply 2

TenOfThem

Original post by Sayless

You factorise and then check either side of the zero values

Here is an example

x^2 + x - 12 > 0

(x-3)(x+4) > 0

The values we are interested in are x=-4 and x=3

Check a value less than -4
x=-5 gives >0

Check between
x=0 gives <0

Check a value above 3
x=4 gives >0

So the solution set is
x<-4 or x>3

TBH you only need to check one as the others follow

(edited 9 years ago)

Reply 3

Sayless

Original post by TenOfThem

You factorise and then check either side of the zero values

Here is an example

x^2 + x - 12 > 0

(x-3)(x+4) > 0

i understand what you did in the first part to get x=-4 and x=-3 but i dont know what to do after that

Reply 4

TenOfThem

Original post by Sayless

i understand what you did in the first part to get x=-4 and x=-3 but i dont know what to do after that

check values either side of -4 and 3

These are the points where the function = 0

Reply 5

MathMeister

Original post by TenOfThem

...

Can you take a graphic calculator into the C1 (edexcel) exam?

Reply 6

Super199

Original post by MathMeister

Can you take a graphic calculator into the C1 (edexcel) exam?

Not allowed a calculator in C1 :smile:

Reply 7

MathMeister

Original post by Super199

Not allowed a calculator in C1 :smile:

Oh yeah

Reply 8

Sayless

Original post by TenOfThem

check values either side of -4 and 3

These are the points where the function = 0

do you put the values of either side of -4 and 3 in the factorised equation to replace x then solve the brackets? im really confused on where the crocodile symbols fit into this

Reply 9

TenOfThem

Original post by Sayless

do you put the values of either side of -4 and 3 in the factorised equation to replace x then solve the brackets? im really confused on where the crocodile symbols fit into this

You put the values into the equation - you can use the original or the factorised as they are the same

Reply 10

Sayless

Original post by TenOfThem

You put the values into the equation - you can use the original or the factorised as they are the same

for my inequality x^2+x-6=< 0
i got (x-2)(x+3)
x=2
x=-3

x=3 gives >0
x=-4 gives >0
x=0 gives >0

where do i go from here

(edited 9 years ago)

Reply 11

TenOfThem

Original post by Sayless

for my inequality x^2+x-6=< 0
i got (x-2)(x+3)
x=2
x=-3

x=3 gives >0
x=-4 gives >0
x=0 gives >0

where do i go from here

Checking something less than -3
You have chosen x = -4
This does give the function >0

Checking something between the values
You have chosen x = 0
When you substitute this into the function what value do you get?

Checking something greater than 2
You have chosen x = 3
This does give the function >0

Since these both give answers >0 those regions are no use to you

Reply 12

Sayless

Original post by TenOfThem

i get the value -6 for x=0

Reply 13

TenOfThem

Original post by Sayless

i get the value -6 for x=0

So why did you say it was >0

It is <0

So that is the section that you want

Reply 14

MrHashim

Original post by Sayless

for my inequality x^2+x-6=< 0
i got (x-2)(x+3)
x=2
x=-3

x=3 gives >0
x=-4 gives >0
x=0 gives >0

where do i go from here

Imagine the graph of x^2 + x - 6 = 0
Positive quadratic with y intercept of -6
Now as the inequality is less than or equal to 0, look for when the graph is less than or equal to 0. In this case it would be between -3 and 2, so the the answer would be -3 =< x =< 2

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