Can anyone tell me how to solve an inequality like this?
.
I tried factorising it like this:
But I don't see how I can solve it from there. I'd just like to know the method please, so I can do it myself thank you.
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Can anyone tell me how to solve an inequality like this?
.
I tried factorising it like this:
But I don't see how I can solve it from there. I'd just like to know the method please, so I can do it myself thank you.
Hello LupinFirst, you need to find the values of that make the function zero. Since you've factorised it, that's now very easy: and .
Next, imagine the number line with these numbers and marked, and the number moving from left to right along the line. When it's right over on the lefthand side, . When it's somewhere in the middle , and when it's going off at the righthand end, . So, look at the signs of your factors and in each of these three ranges of values of . For instance:
When (e.g. ), is negative and is also negative. And a negative times a negative equals a positive. So is positive. Which is not what we want: we want values of that make .
Now look at the other two ranges: and , and see what happens to the signs in each case.
I hope you can finish it now.
Grandad
then so
Here is a gift for you Lupin
Solve for x:
(i)
(ii)
I hope you enjoy working on them.
Hello, Lupin!
Quote:
Can anyone tell me how to solve an inequality like this?
.
I tried factorising it like this: .
But I don't see how I can solve it from there.
We have a parabola: .
It opens upward and has xintercepts 3 and 2.
So it looks like this:Code:
*  *

*  *
  *    +  *     
3 *  * 2
* 

And they are asking: When is the function negative?
. . That is: When is the parabola below the xaxis?
Got it?
Thanks for all the help everyone. I totally understand this now. As for Pankaj's questions:
(i) and
(ii)
I hope they're right, and thanks for the questions.
(i)There appears to be a typo .In place of 2 you should have written 2.
(ii)There is a very simple way out to do such questions.Plot all the numbers on the number line where the factors become zero.Here we see that 4,2,7,11 are the numbers.
The number line gets split into 5 parts/intervals.
() .........(+) .........(+)............... ()................ (+)
Number line
........4 ..........2....... .......7 ...............11...........
Starting from the rightmost interval start putting the (+) and () signs alternatively.But remember sign will not change across that number whose corresponding factor has even power,2 in this case.And you get the desired intervals which are
Remember to exclude 2 since at x=2 LHS becomes 0.Your initial question can be answered in the same manner
read this doc file