I would complete the square in the middle term. What does that do for you?
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
Another technique that's useful is to plot the middle term like this.
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)
Muhammad Abbas
12th grade
Islamia College Peshawar, Pakistan
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.(FOR ACKBEET, dont write "[-8,-6]" its WRONG...write (-8,-6).......i hope u get my point)
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!
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.
Muhammad Abbas Khan
12th grade
Islamia College Peshawar.
There are pens that work in micro-gravity situations, believe me, though I don't require students to use those.
""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
Muhammmad Abbas
Grade 12th
Islamia College Peshawar, Pakistan