# 6.5 Inequalities and graphs

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

This lesson contains 25 slides, with interactive quizzes and text slides.

## Items in this lesson

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

#### Slide 1 -Slide

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 -Slide

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

#### Slide 3 -Drag question

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 -Slide

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

#### Slide 6 -Slide

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 -Slide

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 -Slide

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 -Slide

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 -Slide

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 -Slide

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

#### Slide 12 -Slide

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 -Slide

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 question

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

#### Slide 16 -Slide

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

#### Slide 17 -Slide

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

#### Slide 18 -Slide

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 -Slide

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 -Slide

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 -Slide

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

#### Slide 23 -Slide

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 -Slide

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
<
>