# 6.5 Inequalities and graphs

Good morning!
Schedule:
• 6.5 Learning goals
• Theory
• Work on your homework OR practice together
1 / 25
Slide 1: Tekstslide
WiskundeMiddelbare schoolhavoLeerjaar 3

In deze les zitten 25 slides, met interactieve quizzen en tekstslides.

## Onderdelen in deze les

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

#### Slide 1 -Tekstslide

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 -Tekstslide

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

#### Slide 3 -Sleepvraag

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 5 -Tekstslide

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

#### Slide 6 -Tekstslide

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 -Tekstslide

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 -Tekstslide

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 -Tekstslide

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 -Tekstslide

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 -Tekstslide

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

#### Slide 12 -Tekstslide

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 -Tekstslide

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

What should I fill in for A and for B?

A                                               B

#### Slide 15 -Open vraag

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

#### Slide 16 -Tekstslide

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

#### Slide 17 -Tekstslide

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

#### Slide 18 -Tekstslide

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 -Tekstslide

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 -Tekstslide

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 -Quizvraag

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 -Tekstslide

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

#### Slide 23 -Tekstslide

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 -Tekstslide

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
<
>