6.5 Inequalities and graphs

Good morning!
Schedule: 
  • 6.5 Learning goals  
  • Theory 
  • Questions about 6.4? 
  • Work on your homework OR practice together
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Slide 1: Diapositive
WiskundeMiddelbare schoolhavoLeerjaar 3

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Good morning!
Schedule: 
  • 6.5 Learning goals  
  • Theory 
  • Questions about 6.4? 
  • Work on your homework OR practice together

Slide 1 - Diapositive

Learning goals
At the end of this lesson I can: 
  • Solve a linear inequality 
  • Write intervals with the correct mathematical notations 
  • Solve the inequality of two functions (for example f(x) < g(x)) by looking at their graphs 
<
>

Slide 2 - Diapositive

a > b 
a < b 
Theory A: Linear inequalities 
a is bigger than b
a is smaller than b

Slide 3 - Question de remorquage

Theory A: Linear inequalities
You can draw an arrow, the arrow is always pointing to the smaller number! 




b is smaller than a or a is bigger than b 

a    > b 
a  >  b

Slide 4 - Diapositive

Slide 5 - Diapositive

Cf = 0.3x + 25 
Cs = 0.5x + 12
we want to know when 
Cf < Cs

Slide 6 - Diapositive

Theory A: Linear inequalities 
How to solve a linear inequality: 
1. Move the terms with a x to the left hand side and the rest to the right hand side. 
2. Simplify both sides. 
3. Divide by the number in front of the x. If this number is negative you flip the < or >
1. 


2. 3. 

Slide 7 - Diapositive

Theory A: Linear inequalities 
How to solve a linear inequality: 
1. Move the terms with a x to the left hand side and the rest to the right hand side. 
2. Simplify both sides. 
3. Divide by the number in front of the x. If this number is negative you flip the < or >
0.3x + 25 < 0.5x + 12 
0.3x - 0.5x + 25 < 0.5x - 0.5x + 12 
-0.2x + 25 < 12 
-0.2x + 25 - 25 < 12 - 25   

           


1. 


2. 3. 

Slide 8 - Diapositive

Theory A: Linear inequalities 
How to solve a linear inequality: 
1. Move the terms with a x to the left hand side and the rest to the right hand side. 
2. Simplify both sides. 
3. Divide by the number in front of the x. If this number is negative you flip the < or >
0.3x + 25 < 0.5x + 12 
0.3x - 0.5x + 25 < 0.5x - 0.5x + 12 
-0.2x + 25 < 12 
-0.2x + 25 - 25 < 12 - 25   

-0.2x < -13
          

x > 65
1. 



2. 3. 

Slide 9 - Diapositive

Theory A: Linear inequalities 
How to solve a linear inequality: 
1. Move the terms with a x to the left hand side and the rest to the right hand side. 
2. Simplify both sides. 
3. Divide by the number in front of the x. If this number is negative you flip the < or >
0.3x + 25 < 0.5x + 12 
0.3x - 0.5x + 25 < 0.5x - 0.5x + 12 
-0.2x + 25 < 12 
-0.2x + 25 - 25 < 12 - 25   
-0.2x < -13
           > 

0.20.2x
0.213
1. 


2. 3. 

Slide 10 - Diapositive

Theory A: Linear inequalities 
How to solve a linear inequality: 
1. Move the terms with a x to the left hand side and the rest to the right hand side. 
2. Simplify both sides. 
3. Divide by the number in front of the x. If this number is negative you flip the < or >
0.3x + 25 < 0.5x + 12 
0.3x - 0.5x + 25 < 0.5x - 0.5x + 12 
-0.2x + 25 < 12 
-0.2x + 25 - 25 < 12 - 25   
-0.2x < -13
           > 

x > 65
0.20.2x
0.213
1. 


2. 3. 

Slide 11 - Diapositive

In the graph we see that Flytaxi is indeed cheaper for x > 65!

Slide 12 - Diapositive

Theory B: Intervals
Me and my mom are going to the park. My mom says she will be there in 5-20 minutes. 
If t is the time it takes my mom to get to the park: 

t > 5 and t < 20 
we write this as 
5 ___ t ___ 20 

Slide 13 - Diapositive

Theory B: Intervals
Let's look at the number line: 



What should I fill in for A and for B? 

A                                               B

Slide 14 - Diapositive


Slide 15 - Question ouverte

Theory B: Intervals
Let's look at the number line: 





Slide 16 - Diapositive

Theory B: Intervals
We can write this as: 
x < -2 or x > 4 
x < -2  x > 4 

Slide 17 - Diapositive

Theory C: inequalities and graphs
Solve f(x) < g(x). 

Slide 18 - Diapositive

Theory C: inequalities and graphs
Solve f(x) < g(x). 
we find an interval where the graph of f(x) is SMALLER than g(x). 
At what interval is the graph of f(x) BELOW the graph of g(x)? 

Slide 19 - Diapositive

Theory C: inequalities and graphs
Solve f(x) < g(x). 
We find that f(x) < g(x) at the interval 2 < x < 5. 

What is the interval for
f(x) > g(x)? 

Slide 20 - Diapositive


What is the interval for 
f(x) > g(x) ? 
A
2 > x > 5
B
x < 2
C
x < 2 v x > 5
D
x > 5

Slide 21 - Quiz

Theory C: Inequalities and graphs
How to solve an inequality with a graph (when you don't know the functions): 
1. Find the x-values of the intersection point(s) of the graphs
2. If f(x) > g(x) you look for an interval where the graph of f(x) is ABOVE the graph of g(x). 
 If f(x) < g(x) you look for an interval where the graph of f(x) is BELOW the graph of g(x). 
3. Write down the correct interval. 

Slide 22 - Diapositive

Take out your diaries 


Homework for   8-4-2021:
Havo                  p. 25-30: #44-56

Slide 23 - Diapositive

Raise your hand if: 

You would like to practice with homework sums on the board. 

If you don't raise your hand, you can start on the homework. 

Slide 24 - Diapositive

Learning goals
At the end of this lesson I can: 
  • Solve a linear inequality 
  • Write intervals with the correct mathematical notations 
  • Solve the inequality of two functions (for example f(x) < g(x)) by looking at their graphs 
<
>

Slide 25 - Diapositive