6.5 Inequalities and graphs

• Wiskunde
• Middelbare school
• havo
• Leerjaar 3

Good morning!

Schedule: 

• 6.5 Learning goals  
• Theory 
• Questions about 6.4? 
• Work on your homework OR practice together

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 

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a > b 

a < b 

Theory A: Linear inequalities 

a is bigger than b

a is smaller than b

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

C_f = 0.3x + 25 

C_s = 0.5x + 12

we want to know when 

C_f < C_s

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. 

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. 

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. 

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

           > 

​−0.2​​−0.2x​​

​−0.2​​−13​​

1. 

2. 3. 

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

​−0.2​​−0.2x​​

​−0.2​​−13​​

1. 

2. 3. 

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

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 

Theory B: Intervals

Let's look at the number line: 

What should I fill in for A and for B? 

A                                               B

Theory B: Intervals

Let's look at the number line: 

Theory B: Intervals

We can write this as: 

x < -2 or x > 4 

x < -2  v  x > 4 

Theory C: inequalities and graphs

Solve f(x) < g(x). 

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)? 

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)? 

What is the interval for 

f(x) > g(x) ? 

1. 2 > x > 5
2. x < 2
3. x < 2 v x > 5
4. x > 5

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. 

Take out your diaries 

Homework for   8-4-2021:

Havo                  p. 25-30: #44-56

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. 

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 

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