#1

Well ive got a C1 A-level maths exam coming up tomorrow and im busy revising but ive just found something really simple, confusing.

Ive got an inequality 3x^2 < 2-x and im not sure how to get rid of the sqaured part without buggering up the otherside, some help please

Ive got an inequality 3x^2 < 2-x and im not sure how to get rid of the sqaured part without buggering up the otherside, some help please

#2

Take the square root of both sides right? Then the square on the 3x cancels out and you're left with 3x < sqrt 2-x. I don't know, it's been a while since I've seen inequalities...

*Last edited by jasonmetal love at Jan 10, 2010,*

#3

Just take the square root. Nothing changes to the inequality sign

EDIT: took a better looks at the equation... Just leave the squared and make the equation 3x^2 + x - 2 < 0.

I'm sure you can solve that

EDIT: took a better looks at the equation... Just leave the squared and make the equation 3x^2 + x - 2 < 0.

I'm sure you can solve that

*Last edited by basilbrush at Jan 10, 2010,*

#4

first you would make it 3x^2+x-2<0

and then solve it as a normal quadratic equation from there but remember to have the smaller than sign still in otheriwse you lose marks for putting = rather than <

and then solve it as a normal quadratic equation from there but remember to have the smaller than sign still in otheriwse you lose marks for putting = rather than <

#5

yeah i was ganna do that, but ive got to work out x so im only wanting the x's on one side

#6

I think you need to turn it into a quadratic inequality.

Take 2-x away from both sides, giving you:

3x^2+x-2<0.

Then you just solve that and you've got the answer.

Take 2-x away from both sides, giving you:

3x^2+x-2<0.

Then you just solve that and you've got the answer.

#7

Math does NOT get me turned on, that's for sure.

#8

yeah, ive got it sussed now, thanks guys

#9

Make it 3X^2+x-2<0

Factorise

You will probably get two inequalities for x

I have C3 in a few days

Factorise

You will probably get two inequalities for x

I have C3 in a few days

#10

(x+1)(3x-2)<0

-1<x<2/3

Hope that helps.

-1<x<2/3

Hope that helps.

#11

I have C3 in a few days

Is that the second year of A levels?

#12

(x+1)(3x-2)<0

-1<x<2/3

Hope that helps.

Thanks, but now im not too sure about how you tell which way the inequalities are facing as in toward or away from the X '-1<x<2/3'

#13

Well ive got a C1 A-level maths exam coming up tomorrow and im busy revising but ive just found something really simple, confusing.

Ive got an inequality 3x^2 < 2-x and im not sure how to get rid of the sqaured part without buggering up the otherside, some help please

I have the same exam, good luck brah.

Don't need to get rid of it because its a quadratic.

3x^2 +x -2 < 0

Factorise. (3x-2)(x+1)<0

Solve each bracket equal to zero for roots (answer equation)

3x-2 < 0

3x<2

x<2/3

or

x+1<0

x<-1

Also with inequalities remember if dividing or multiplying by a negative you swap the sign. i.e < goes to >

#14

Thanks, but now im not too sure about how you tell which way the inequalities are facing as in toward or away from the X '-1<x<2/3'

Sketch the graph and it becomes obvious.

Here's a good site for it

http://www.wolframalpha.com/input/?i=3x^2-2%2Bx+%3C0

Okay from that its clearly -1<x<2/3

Which is the shaded region on that graph, because remember the original thing was:

Equation < 0

Less than zero is everything under the graph.

*Last edited by Pipsicles at Jan 10, 2010,*

#15

I have the same exam, good luck brah.

Don't need to get rid of it because its a quadratic.

3x^2 +x -2 < 0

Factorise. (3x-2)(x+1)<0

Solve each bracket equal to zero for roots (answer equation)

3x-2 < 0

3x<2

x<2/3

or

x+1<0

x<-1

Also with inequalities remember if dividing or multiplying by a negative you swap the sign. i.e < goes to >

Thanks , good luck to you too