2Tvwo §9.4 Solving inequalities (1)

• Wiskunde
• Middelbare school
• vwo
• Leerjaar 2

§9.4 Solving inequalities

(ongelijkheden)

Up to now we only dealt with equations, so:                  

              'something being equal to something else'.

2c + 5 = 6c

However,  

something could also be GREATER THAN or SMALLER THAN                                      something else!

Below you see what you will learn and the kind of tasks 

you are going to solve. But how?! 

Do you remember the signs:

           for 'smaller than'       and 

           for 'greater than'?

In this lesson .....

+ we will march through the first part of §9.4 together

+ homework will be p.102:           29, 30 and 31 

            (only 3 exercises? Yes, but this is still a lotta work!)

Next slide has a long text. Read this for yourself first.

Of course you can take your own book 2B, p.100 , where it's from!

jk

Answer the 1st question only, so:

Is it possible that the bags each contain 4 marbles?

Make a calculation in your head (or on paper) and key in your answer in the next slide!

1. yes
2. no

Answer and explanation:

No!            Why not?       Look below:

 Keep in mind that the left side is heavier, so it contains more marbles!

jk

Answer this question now:

'Is it possible that the bags each contain 8 marbles?'

Make a CALCULATION in your NOTEBOOK

and key in your answer in the next slide!

Is 8 marbles possible?!

Answer and explanation:

The good answer is:                Yes!              Explanation follows:

Why is this 8 marbles a good answer? 

Because the left side then is heavier as it contains more marbles!

A balance or a graph...

For an amazing balance, watch next slide!

We are going to do 27 now.  It is much handier to work from the paper book, p.101, of course!

And now, bit by bit...

Work out in your Notebook now!

Make in your Notebook:

Task:

Solution:

Task:

Make in your Notebook and then

key in your answer in the next slide!

Graph A is steeper because ...
(tell from the formulas!)

Answer 27 c:

Task:

         Make in your Notebook and compare a bit later!

Task:

Solution:

Task:

Make in your Notebook and

compare, soon.

                     

You have been doing great up to now!

This LessonUp takes a lot of our time, but remember:

pages 100 and 101 we have almost finished now!

Finally here comes the METHOD how to 

SOLVE an INEQUALITY (ongelijkheid).

From now on, it's 'the other way around':

We DON'T HAVE A GRAPH, but just an INEQUALITY! 

Oh dear, how sad, never mind... There's  great SOLUTION to this 'problem':

In order to SOLVE this, 

we will MAKE a SKETCH of the two graphs ourselves.

Next slides show how to do all this!

The first two steps are done in order to:

calculate the point of intersection (=p.o.i.) of the graphs!

The following slides shows you an example of this METHOD!

Then the points 1, 2, 3 and 4 correspond to those above!

What does this task mean?

It asks for all the x numbers for which the GRAPH for

y = x + 10 lies higher than the one for y = 2x + 2

There's some work to be done for this, as we don't have the graphs?! Next slides explain it all! 

What is the next step to take?

After all is said and done ...

There are exercises 29, 30 and 31 to be done by yourself.

In 29 and 30 no graphs are given, so just 

+ work out the 4 points from the Method we just went through;

+ this Method is there for you on pages 101 and 102!

Homework time

DO:

§9.4:      29, 30 and 31