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2Tvwo §9.4 Solving inequalities (1)
§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!
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Wiskunde
Middelbare school
vwo
Leerjaar 2
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37 slides
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interactive quizzes
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Lesson duration is:
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§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!
Slide 1 - Slide
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'?
Slide 2 - Slide
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!
Slide 3 - Slide
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!
Slide 4 - Slide
A
yes
B
no
Slide 5 - Quiz
Answer and explanation:
No! Why not? Look below:
Keep in mind that the left side is heavier, so it contains more marbles!
Slide 6 - Slide
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!
Slide 7 - Slide
timer
1:00
Is 8 marbles possible?!
Slide 8 - Mind map
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!
Slide 9 - Slide
A balance or a graph...
For an amazing balance, watch next slide!
Slide 10 - Slide
Slide 11 - Slide
We are going to do 27 now. It is much handier to work from the paper book, p.101, of course!
Slide 12 - Slide
And now, bit by bit...
Work out in your Notebook now!
timer
1:30
Slide 13 - Slide
Slide 14 - Slide
Make in your Notebook:
timer
0:30
Slide 15 - Slide
Task:
Solution:
Slide 16 - Slide
Task:
Make in your Notebook and then
key in your answer in the next slide!
timer
1:00
Slide 17 - Slide
Graph A is steeper because ...
(tell from the formulas!)
Slide 18 - Mind map
Answer 27 c:
Slide 19 - Slide
Task:
Make in your Notebook and compare a bit later!
timer
0:30
Slide 20 - Slide
Task:
Solution:
Slide 21 - Slide
Task:
Make in your Notebook and
compare, soon.
timer
0:30
Slide 22 - Slide
Slide 23 - Slide
Slide 24 - Slide
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).
Slide 25 - Slide
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!
Slide 26 - Slide
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!
Slide 27 - Slide
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!
Slide 28 - Slide
Slide 29 - Slide
Slide 30 - Slide
Slide 31 - Slide
What is the next step to take?
Slide 32 - Mind map
Slide 33 - Slide
Slide 34 - Slide
Slide 35 - Slide
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!
Slide 36 - Slide
Homework time
DO:
§9.4: 29, 30 and 31
Slide 37 - Slide
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