1. Math 51
2.1, 2.2, 2.3
Linear Equations

2. Linear Equations
A linear equation in one variable (𝑥) is an equation that can be written in the form: ________________________________________ ex: 2𝑥+3=17 is a linear equation 𝑥 2 +2𝑥=5 is not a linear equation 1 𝑥 =6 is not a linear equation 2𝑥+6 =0 is not a linear equation

3. Linear Equations 𝑨𝒙+𝑩=𝑪 (where 𝑨≠𝟎)
A linear equation in one variable (𝑥) is an equation that can be written in the form: ________________________________________ ex: 2𝑥+3=17 is a linear equation 𝑥 2 +2𝑥=5 is not a linear equation 1 𝑥 =6 is not a linear equation 2𝑥+6 =0 is not a linear equation
𝑨𝒙+𝑩=𝑪 (where 𝑨≠𝟎)

4. Linear Equations 𝑨𝒙+𝑩=𝑪 (where 𝑨≠𝟎)
A linear equation in one variable (𝑥) is an equation that can be written in the form: ________________________________________ ex: 2𝑥+3=17 is a linear equation 𝑥 2 +2𝑥=5 is not a linear equation 1 𝑥 =6 is not a linear equation 2𝑥+6 =0 is not a linear equation
𝑨𝒙+𝑩=𝑪 (where 𝑨≠𝟎)

5. Linear Equations 𝑨𝒙+𝑩=𝑪 (where 𝑨≠𝟎)
A linear equation in one variable (𝑥) is an equation that can be written in the form: ________________________________________ ex: 2𝑥+3=17 is a linear equation 𝑥 2 +2𝑥=5 is not a linear equation 1 𝑥 =6 is not a linear equation 2𝑥+6 =0 is not a linear equation
𝑨𝒙+𝑩=𝑪 (where 𝑨≠𝟎)

6. Linear Equations 𝑨𝒙+𝑩=𝑪 (where 𝑨≠𝟎)
A linear equation in one variable (𝑥) is an equation that can be written in the form: ________________________________________ ex: 2𝑥+3=17 is a linear equation 𝑥 2 +2𝑥=5 is not a linear equation 1 𝑥 =6 is not a linear equation 2𝑥+6 =0 is not a linear equation
𝑨𝒙+𝑩=𝑪 (where 𝑨≠𝟎)

7. Linear Equations 𝑨𝒙+𝑩=𝑪 (where 𝑨≠𝟎)
A linear equation in one variable (𝑥) is an equation that can be written in the form: ________________________________________ ex: 2𝑥+3=17 is a linear equation 𝑥 2 +2𝑥=5 is not a linear equation 1 𝑥 =6 is not a linear equation 2𝑥+6 =0 is not a linear equation
𝑨𝒙+𝑩=𝑪 (where 𝑨≠𝟎)

8. Linear Equations
Ex 1. Solve and check: 2𝑥+3=17

9. Examples of sets
5,7,8,10,27
2,−1
1,2,3 ={2,1,3}
{} or ∅ means empty set
ℝ means the set of all real #’s
(ex: 0, 3, 1 2 , −0.2, 𝜋, …)

10. Examples of sets
5,7,8,10,27
2,−1
1,2,3 ={2,1,3}
{} or ∅ means empty set
ℝ means the set of all real #’s
(ex: 0, 3, 1 2 , −0.2, 𝜋, …)

11. Examples of sets
5,7,8,10,27
2,−1
1,2,3 ={2,1,3}
{} or ∅ means empty set
ℝ means the set of all real #’s
(ex: 0, 3, 1 2 , −0.2, 𝜋, …)

12. Examples of sets
5,7,8,10,27
2,−1
1,2,3 ={2,1,3}
{} or ∅ means empty set
ℝ means the set of all real #’s
(ex: 0, 3, 1 2 , −0.2, 𝜋, …)

13. Examples of sets
5,7,8,10,27
2,−1
1,2,3 ={2,1,3}
{} or ∅ means empty set
ℝ means the set of all real #’s
(ex: 0, 3, 1 2 , −0.2, 𝜋, …)

14. Linear Equations
__________ both sides.
_______________ so that variable terms are on one side, and constants are on the other.
3. __________ by coefficient of variable term.

15. Linear Equations
__________ both sides.
_______________ so that variable terms are on one side, and constants are on the other.
3. __________ by coefficient of variable term.
Simplify

16. Linear Equations
__________ both sides.
_______________ so that variable terms are on one side, and constants are on the other.
3. __________ by coefficient of variable term.
Simplify
Add/subtract

17. Linear Equations
__________ both sides.
_______________ so that variable terms are on one side, and constants are on the other.
3. __________ by coefficient of variable term.
Simplify
Add/subtract
Divide

18. Linear Equations
__________ both sides.
_______________ so that variable terms are on one side, and constants are on the other.
3. __________ by coefficient of variable term.
Simplify
Add/subtract
Divide

19. Linear Equations
Ex 2. Solve and check: 2𝑥+5−𝑥=2𝑥+13+3𝑥 Ex 3. Solve and check: 2 𝑥−1 +3=𝑥−3 𝑥+1 Ex 4. Solve and check: 1 4 𝑥+1 = −𝑥

20. Linear Equations
Ex 5. Try to solve: 𝑥+3=𝑥+2+1. What happened, and what does it mean? Ex 6. Now try to solve: 𝑥=𝑥+7. What happened this time, and what does it mean?

21. Linear Equations
An equation that is ____________ true is called an ________________________. An equation that is ____________ true is called a ______________________________________. An equation that is ____________ true is called a _______________________________________.

22. Linear Equations
An equation that is ____________ true is called an ________________________. An equation that is ____________ true is called a ______________________________________. An equation that is ____________ true is called a _______________________________________.
always

23. Linear Equations
An equation that is ____________ true is called an ________________________. An equation that is ____________ true is called a ______________________________________. An equation that is ____________ true is called a _______________________________________.
always
identity

24. Linear Equations
An equation that is ____________ true is called an ________________________. An equation that is ____________ true is called a ______________________________________. An equation that is ____________ true is called a _______________________________________.
always
identity
sometimes

25. Linear Equations
An equation that is ____________ true is called an ________________________. An equation that is ____________ true is called a ______________________________________. An equation that is ____________ true is called a _______________________________________.
always
identity
sometimes
conditional equation

26. Linear Equations
An equation that is ____________ true is called an ________________________. An equation that is ____________ true is called a ______________________________________. An equation that is ____________ true is called a _______________________________________.
always
identity
sometimes
conditional equation
never

27. Linear Equations
An equation that is ____________ true is called an ________________________. An equation that is ____________ true is called a ______________________________________. An equation that is ____________ true is called a _______________________________________.
always
identity
sometimes
conditional equation
never
contradiction