1. Using the numbers {-2, -1, 0, 1, 2} Solve the following equations.
1.) -2x = 2
2.) 3x = x + 4
3.) x = 4/x

2. Using the numbers {-2, -1, 0, 1, 2} Solve the following equations.
1.) -2x = ) 3x = x + 4
-2(-2) = (-2) =
-2(-1) = (-1) =
-2(0) = (0) =
-2(1) = (1) =
-2(2) = (2) = F F T F F F F F F T

3. Using the numbers {-2, -1, 0, 1, 2} Solve the following equations.
3.) x = 4/x
-2 = 4/-2
-1 = 4/-1
0 = 4/0
1 = 4/1
2 = 4/2
True
False
False
False
True

4. Bellwork 9/24
Using the numbers {-2, -1, 0, 1, 2} Solve the following equations.
Since -1 makes
1.) -2x = 2
-2(-1) = 2
2 = 2
the equation true,
it is the solution.

5. Bellwork 9/24
Using the numbers {-2, -1, 0, 1, 2} Solve the following equations.
Since 2 makes
2.) 3x = x+4
3(2) = 2 + 4
6 = 6
the equation true,
it is the solution.

6. Bellwork 9/24
Using the numbers {-2, -1, 0, 1, 2} Solve the following equations.
3.) x = 4/x
AND
-2 = 4/-2
-2 = -2

7. Bellwork 9/24
Using the numbers {-2, -1, 0, 1, 2} Solve the following equations.
Since 2 & -2 make
3.) x = 4/x
2 = 4/2
2 = 2
the equation true,
they are solutions.

8. Today’s Objective
To be able to recognize equations that are equivalent to other equations….
Understanding how to make the BEST FIRST STEP (the BFS)

9. Take good notes Today
This icon,
Means to take notes

10. Suppose ….. (Pizza Pizza)
You and 3 of your friends ordered a pizza. The cost of the pizza was $ How could you write an equation to determine the cost for each of the 4 people?

11. Techniques and strategies for solving equations.
Up to this point you have been using:
a.)Mental Math to solve equations.
b.)Substitution to solve equations
Now we will look at strategies

12. Equ
Equivalent Equations al
Equivalent Equations are equations that look different, but have the same solutions…
Example:
2x = and x + 1 = 9
Take Notes

13. We will show these equations to be equivalent with the number (4)
they must be equivlalent
1.) 2x = x + 1 = 9
Since both equations are True for 4,
2(4) = (4) + 1 = 9
8 = = 9
9 = 9 T T

14. Equations
Expressions
Equations are made up of two (2) Expressions separated by an equal (=) sign.
Example: 2x + 3x = 30
Equal sign

15. Equations must maintain a BALANCE
What you do
to one side
must be done
to the other

16. Start with x - 7 = 3 Simplify: x - 2 = 8 This NEW equation
Add 5 to both sides: x-7+5 = 3+5
Simplify: x - 2 = 8
This NEW equation
is equivalent to the FIRST equation. Because x = 10

17. Now Consider x - 7 = 3 Simplify: x = 10
Add 7 to both sides: x-7+7 = 3+7
Simplify: x = 10
Of These two examples which one simplifies the equation the most???

18. Start with a + 3 = 1 Simplify: a = -2
Subtract 3 from : a = 1 -3
Simplify: a = -2
Why did we subtract 3 from both sides of the equation??
Subtracting 3 is the BFS

19. Determining the BEST FIRST STEP (BFS)
The BFS is the step that will simplify the equation in the least amount of steps.
In 1 step equations, it is usually the inverse operation.

20. Start with 1/2y = 6 (2)1/2y = (2)6 Simplify: y = 12
Multiply both sides by 2 :
(2)1/2y = (2)6
Simplify: y = 12
Why did we multiply both sides by 2 ??
Multiplying by 2 is the BFS

21. Start with -3m = 12 -3m/-3 = 12/-3 Simplify: m = -4
Divide both sides by -3 :
-3m/-3 = 12/-3
Simplify: m = -4
Why did we divide both sides by -3 ??
Dividing by -3 is the BFS

22. What does all this mean ?
An Equivalent Equation is obtained when you add, subtract, multiply, or divide the same number to BOTH SIDES of the equation.
BUT REMEMBER,

23. You can do what ever you want to an equation, as long as you do it to both sides!
So the TRICK is to determine the BFS to make solving equations easier, faster, and simpler

24. Be Ready to Answer the Following:
1.) What’s the difference between an Expression and an Equation?
2.) What separates the 2 expressions of an equation?
3.) You can do anything you want to an equation as long as _____?
4.) What’s BFS?

25. What’s the Best First Step
1.) 3x = 6
2.) x - 8 = 7
3.) a + 5 = 9
4.) x/3 = 9
Divide by 3
Add 8
Subtract 5
Multiply by 3

26. What’s the Best First Step
5.) -2x = 8
6.) 2x = 7
7.) ½a = 9
8.) -3x = 9
Divide by -2
Divide by 2
Mult by 2
Divide by -3

27. What’s the Best First Step
9.) 3x - 5x = 6
10.) 2x - 8 = 6
11.) a + 5 = 9
12.) x/3 + 6 = 9
CLT
Add 8
Sub 5
Sub 6

28. Now for the steps 1.) Simplify each side of the equation.
2.) Get the Variables together first.
3.) Then, get the Whole Numbers together.
4.) Finally, get the variable by itself.

29. Now you try these Show all work on page 3
1.) 3x = 6
2.) x - 8 = 7
3.) a + 5 = 9
4.) x/3 = 9

30. Now you try these 1.) 3x = 6 3x/3 = 6/3 x = 2 2.) x - 8 = 7

31. Now you try these 3.) a + 5 = 9 a + 5 - 5 = 9 - 5 a = 4 4.) x/3 = 9

32. Now back to the Pizza Pizza Problem
You and 3 of your friends ordered a pizza. The cost of the pizza was $ How could you write an equation to determine the cost for each of the 4 people?

33. Pizza Pizza Let x = your cost Then 4x = the cost of all 4 people
So…. 4x = 16.80
4x/4 = 16.80/4
Divide both
sides by 4
x = 4.20
Classwork

34. Follow the directions in order
4x - 5 = 15
1.) Add 5 to both sides
2.) Divide both sides by 4
1.) 4x =
4x = 20
2.) x/4 = 20/4
x = 5

35. Follow the directions in order
1/2x -12 = 18
1.) Add 12 to both sides
2.) Multiply both sides by 2
1.) 1/2x =
1/2x = 30
2.) (2)1/2x = 30(2)
x = 60

36. Classwork
Do worksheet 3.1
Homework
Page 126 (1-12 & ev)

37. Bellwork (Show all work)
9/27
1.) 4x = -24
2.) x - 9 = 14
3.) a + 15 = 9
4.) x/2 = 12

38. Now you try these 1.) 4x = -24 4x/4 = -24/4 x = -6 2.) x - 9 = 14

39. Now you try these 3.) a + 15 = 9 a + 15 - 15 = 9 - 15 a = -6
4.) x/2 = 12
(2)x/2 = 12(2)
x = 24

40. Bellwork (Show all work)
9/29
1.) -3x = -24
2.) x - 7 = 4
3.) a - 8 = 8
4.) 1/2x = 12

41. (Show all work) 1.) -3x = -24 -3x/-3 = -24/-3 x = 8 2.) x - 7 = 4

42. Bellwork (Show all work)
4.) 1/2x = 12
(2)1/2x = 12(2)
x = 24

43. Solve the following Equations Show your work
5.) 10x = 100
x = 10
6.) 256 = 16c
16 = c

44. Solve the following Equations Show your work
7.) 1/2x = -40
x = -80
8.) 3/4L = 75
L = 100
9.) -6x = -36
x = 6
10.) x =
x = 8
11.) c =
c = 105

45. Follow the directions in order
4x - 5 = 15
1.) Add 5 to both sides
2.) Divide both sides by 4
1.) 4x =
4x = 20
2.) x/4 = 20/4
x = 5

46. Follow the directions in order
1/2x -12 = 18
1.) Add 12 to both sides
2.) Multiply both sides by 2
1.) 1/2x =
1/2x = 30
2.) (2)1/2x = 30(2)
x = 60

47. homework
See Side Board