Inequalities

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Probability

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In years gone by I've covered this subject and now returned to it as revision. It appears that although there is much I do understand about inequalities, there is some areas that I don't!

The inequality signs are NOT an issue for understanding.

Where I seem to be having my understanding incorrectly placed is when I am trying to use the inequality number lines with the solid and empty circles at the ends of each line, and which way I am suppose to interpret them in use!

I've tried some examples and I seem not in a position to answer them correctly. Here is my work;

Using inequality signs. Use number lines to represent each of the following inequalities.

a > - 3, b < 6, c < - 2.5

In the first example I draw the line from left to right and include a empty 0 part of the line to show that it is a strict inequality

In the second example I draw the line from left to right but include a solid 0 at the right hand end of the line. This means that the solid circle is contained in the interval

On the third example I draw the line from left to right and use a empty 0 at the left hand end of the line inline with - 2.5.

Without looking back at my last incorrect answers from a few hours ago and then compare my second lot of answers only to find that I have made the same mistakes.

I clearly think I understand it but don't on a practical level.

Are we saying that as far as inequalities are concerned that (< or >) represent strict inequalities, and the (< or >) represent that the numbers are at the limit of the inequality and would be contained in the interval.

Have I got that understanding correct?
 
You have it right with the 'Are we saying that as far as inequalities are concerned that (< or >) represent strict inequalities, and the (< or >) represent that the numbers are at the limit of the inequality and would be contained in the interval. '

That means that we will have a solid circle on your first and last example.

However, where the lines should be drawn, I believe you got it mixed up. If a is bigger or equal to -3, the line will go to the right of your solid circle. if b is smaller than 6, the line will go at the left of your empty circle. And if c is smaller or equal to -2.5, the line will go at the left of your solid circle.
 
Thank you can I add this attachment and ask how I determine which way the arrows should be drawn?Capture of inequality.PNG
 
Smaller means at the left, while bigger means at the right. So for c equal or smaller than -2.5, the line goes at the left of the full circle
So your drawing, is on point :)
 
C is less than or equal to -2.5. Now the big question. Are numbers to the left of -2.5 less than 2.5 OR are numbers to right of -2.5 less than -2.5. What do you think?
 
Thank you for the post Jomo. As I advised at the outset, the inequalities were not the problem for my understanding, and nor is the negative numbers and their arrangements. Like if you looked at your bank account and it said - £ 500 when you thought you had £500, I think most people would know with common sense which is the larger sum in their bank account.

If anyone has problems understanding which negative number is larger or smaller than another, just turn it into money in your bank, you'll soon figure it out :)
 
Your OP talks about endpoints yet your last post post talks about the direction of the arrow. You need to decide which you want help with.
 
yes that was because I had not got to grips with understanding which way to draw the arrow when I was either including the endpoint or not.
 
Probability said:
Thank you can I add this attachment and ask how I determine which way the arrows should be drawn?View attachment 18351
Click to expand...
The statement is:

C is "smaller than" or "equal to" -2.5

Now we ask:

Is -1 smaller than -2.5?

No! - so C cannot reside on this side. The arrow CANNOT point from -2.5 to -1.

Is -3 smaller than -2.5?

Yes! - so C can reside on this side. The arrow CAN point from -2.5 to -3.
 
I think that it doesn't make any sense at all to talk about "left" or "right" of a number until after you have specified that you are talking about a "number line". And even then you have to specify how that number line is oriented. The convention is that smaller numbers are to the left and larger numbers to the right but that is purely arbitrary.
 
HallsofIvy said:
I think that it doesn't make any sense at all to talk about "left" or "right" of a number until after you have specified that you are talking about a "number line". And even then you have to specify how that number line is oriented. The convention is that smaller numbers are to the left and larger numbers to the right but that is purely arbitrary.
Click to expand...
Thanks, it was the direction of the line that it should be drawn in that was the confusion.
 
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