01: linear inequalities

• Wiskunde
• Middelbare school
• vwo
• Leerjaar 3

Goals:

• What is an interval?
  
• What is an inequality?
• How to solve a linear inequality?
  

multiple choice verwacht maar één antwoord ook als er meerder antwoorden zijn

What is an interval?

An interval is a continuous section of a number line.

example:

Which values are in this interval?

1. −2
2. 1
3. 0
4. ​2​​1​​

What about -1 or 2?

Open circle means they are not part of the interval. Filled in circle means they are.

What values are in this interval?

1. 2
2. −1​2​​1​​
3. −2
4. 1​2​​1​​

What values are in this interval?

1. 2
2. −2
3. −1
4. −300

We can write this down as:

x<2

We can write this down as:

We can write this down as:

We can write this down as:

x>−1

For which values is the following true?

x>3

1. x=4
2. x=−3
3. x=1
4. x=3

For which values is the following true?

x<4

1. x=4
2. x=5
3. x=1
4. x=3

For which values is the following true?

x+1>2

1. x=2
2. x=3
3. x=1
4. x=−2

Let's fix this:

x+1>2

−1

−1

x>1

What is an inequality?

We just saw one. :D

How to solve a linear inequality?

2x+3<9

2x+3<9

Solve

5x+7>2x+73

5x+7>8x+73

So what happened?

• We multiplied/ divided with a negative number.
• Solution: flip the sign
  

5x+7>8x+73

Solving (linear) inequalities:

We are allowed to:

• add/ subtract
• a constant? yes
• a variable? yes
• multiply/ divide
• a constant? positive: yes | negative: flip the sign
• a variable? NO
  

Solving (linear) inequalities:

We are allowed to:

• add/ subtract
• a constant? yes
• a variable? yes
• multiply/ divide
• a constant? positive: yes | negative: flip the sign
• a variable? NO
  

Exercises for this lesson:
 6, 8, 9, 11, 12, 13, 14