# Inequality Problem

• Oct 20th 2010, 09:02 AM
StevieGwonder
Inequality Problem
I have taken A-Level maths and im stuck on a question that involves a quadratic inequality

The question is;

18<x^2 + 3x<40

Ive been trying for hours to solve it but I just cant seem to do it.

Thanks

Steve
• Oct 20th 2010, 09:18 AM
Ackbeet
I would complete the square in the middle term. What does that do for you?
• Oct 20th 2010, 09:58 AM
StevieGwonder
It does work. I do it by factorising. However the answers im getting do not seem to make sense. The two different inequalities are;

x<-6 or x>3 and -8<x<5

When I compare these, the only range that is linked with each other is

-8<x<-6
and
3<x<5

However the answer is one inequlity and not two
• Oct 20th 2010, 10:14 AM
Ackbeet
Pick a number in [-8,-6], and see if it satisfies the original inequality. In problems like these, you should ALWAYS check your work this way.
• Oct 20th 2010, 10:17 AM
Ackbeet
Another technique that's useful is to plot the middle term like this.
• Oct 20th 2010, 12:08 PM
khamaar
Look...Just rip the inequality apart.

i) x^2 + 3x < 40
ii)x^2 + 3x >18

Now solve by factorization both equations.
You get these solutions.
i) x<-8
ii) x<5
iii) x>-6
iv) x>3

Now you have to make two combinations from these four solutions (cuz you want to get two solutions, since the inequality was quadratic)

The two solutions formed (through logic) are.

i) -6<x<-8
ii) 3<x<5

Now "Check" both. Just put "-5" in the quality (which belongs to .i. solution) and u see that the inequality is not true.

If u check the other one (ii) you would see that it satisfies the inequality,
Hence the solution is

3<x<5

(FOR ACKBEET, dont write "[-8,-6]" its WRONG...write (-8,-6).......i hope u get my point)

Islamia College Peshawar, Pakistan
• Oct 20th 2010, 12:14 PM
Ackbeet
Quote:

(FOR ACKBEET, dont write "[-8,-6]" its WRONG...write (-8,-6).......i hope u get my point)
It's not wrong if you only regard it as an intermediate step. I would always check the endpoints of an answer anyway, at which point the inclusion or exclusion of the endpoints would become clear.
• Oct 21st 2010, 06:18 AM
khamaar
its ok..i understand... Actually we here, do math with paper and a pencil. And thats why we note such mistakes...I learned from You. I respect you Alot. (Ackbeet)
• Oct 21st 2010, 08:21 AM
Ackbeet
I actually prefer pen to pencil, for a number of reasons:

1. It forces you to make a statement.
2. It is the way scientific lab notebooks are done, for legal reasons.
3. I actually find that it is neater than pencil. If you make a mistake, you draw a box around the mistake, and cross it out. Paper is really not that much of an object these days.

When I was teaching, I made my students do their work in pen. They didn't care for it much, but it is a far better presentation, I can tell you!
• Oct 22nd 2010, 04:55 AM
khamaar
Actually i Have a broader mind, and i use tools which have a "broad range of use". Your students' pens would not work if they are doing math in outer space ( where there are zero gravity conditions ). I, and my students, however, would not have this problem, as long as we have pencils in our hands.

:D

Islamia College Peshawar.
• Oct 22nd 2010, 04:58 AM
Ackbeet
There are pens that work in micro-gravity situations, believe me, though I don't require students to use those.
• Oct 22nd 2010, 10:56 AM
khamaar
""The Fisher Pen Company reportedly invested about \$1 million of its own funds in the effort then patented its product and cornered the market as a result (First space pen made for NASA)""

But, didn't anyone think about a pencil? Maybe you people could have built a third WTC with that Million bux in those years,

(Still sticking with the pencil)
And where is the poster? :S