Year 12s: what will be the first way you research your future options? >>

Inequalities on Graphs

Can someone please explain just how you do it once? For example solving the inequality x²-4x+3 <0? I know to factorise it in which it would be (x-3) (x-1), but where do I go from here?

Scroll to see replies

Reply 1

username1302246

If I remember correctly, you should treat it like a quadratic equation.

(x-3)(x-1) = 0

so, x = 3
and, x = 1

(edited 9 years ago)

Reply 2

Caseyleia

Original post by HarrisxK

If I remember correctly, you should treat it like a quadratic equation.

(x-3)(x-1) = 0

so, x = 3
and, x = 1

I got the answer 1<x<3; is this correct?

Reply 3

TenOfThem

Original post by Caseyleia

I got the answer 1<x<3; is this correct?

yes

Reply 4

username1302246

Original post by Caseyleia

I got the answer 1<x<3; is this correct?

Yes, that is correct :biggrin:

Reply 5

Caseyleia

Original post by TenOfThem

yes

Thank you! Quick question, where the equation looks like this: 2x²-5x+2>0; I factorised to (2x-1) (x-2) and got the points x= 0.5 and x=2; but I'm not sure which parts I would be using? I put x<0.5 or x>2 but I know that's wrong :rolleyes:

Reply 6

Caseyleia

Original post by HarrisxK

Yes, that is correct :biggrin:

Thank you! Shame they get harder from now! I am not a fan of graph questions!

Reply 7

TenOfThem

Original post by Caseyleia

That answer is correct - why did you think it was wrong

do you know what the graph looks like

Reply 8

Caseyleia

Original post by TenOfThem

That answer is correct - why did you think it was wrong

do you know what the graph looks like

I thought it was wrong because I can do them without the graph? I just do it in my head? And yes I have the graph in front of me, but I just get a bit confused in terms of x>0 and x<0 :colondollar:

Reply 9

TenOfThem

Original post by Caseyleia

I thought it was wrong because I can do them without the graph? I just do it in my head? And yes I have the graph in front of me, but I just get a bit confused in terms of x>0 and x<0 :colondollar:

What do you "do" in your head - there are a number of ways to solve these - I would never draw a graph but you seemed to think it was a graph question

Reply 10

Caseyleia

Original post by TenOfThem

What do you "do" in your head - there are a number of ways to solve these - I would never draw a graph but you seemed to think it was a graph question

I factorise it and use sort of just put them in and order, its hard to explain, but is it okay if I work out the next two and ask you if they're correct?

Reply 11

TenOfThem

Original post by Caseyleia

but is it okay if I work out the next two and ask you if they're correct?

sure

Reply 12

Caseyleia

Original post by TenOfThem

sure

On the next one, the equation was 4x²-20x+25>0; which I factorised as (2x-5) (2x-5). This however gives me the exact same points x=2.5 and x=2.5; did I factorise wrong?

Reply 13

TenOfThem

Original post by Caseyleia

On the next one, the equation was 4x²-20x+25>0; which I factorised as (2x-5) (2x-5). This however gives me the exact same points x=2.5 and x=2.5; did I factorise wrong?

no, that is correct

Reply 14

Caseyleia

Original post by TenOfThem

no, that is correct

Would the answer then be x<2.5 and x>2.5?

Reply 15

TenOfThem

Original post by Caseyleia

Would the answer then be x<2.5 and x>2.5?

well, yes

but you will want to put

x \not= 2.5

Reply 16

Caseyleia

Original post by TenOfThem

well, yes

but you will want to put

x \not= 2.5

Thank you! With your help I really am understanding at final last! I have more of these, and then I have 2 of them to leave in surd form, then I have finished all 100!

Reply 17

TenOfThem

Original post by Caseyleia

Thank you! With your help I really am understanding at final last! I have more of these, and then I have 2 of them to leave in surd form, then I have finished all 100!

Is this pre-A'level work?

Reply 18

Caseyleia

Original post by TenOfThem

Is this pre-A'level work?

Yes, but I have been told it is GCSE work that we're going over, except I didn't do work half this hard at GCSE and I got an A?!
The next one is 3x² - x > 0; they're getting much easier now :smile:

Reply 19

Quantum Confinement

Original post by Caseyleia

Can someone please explain just how you do it once? For example solving the inequality x²-4x+3 <0? I know to factorise it in which it would be (x-3) (x-1), but where do I go from here?