1. Lesson 3.2: Introduction to Solving Equations
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2. 3). You are having pizzas delivered. How much is each pizza?
Picture
Equation + =
3x =
24.75
4.00 ?
_________ =
24.75
3x =
24.75
24.75
= 8.25
x =
8.25 3 =
8.25

3. Two bottles of root beer and a $3 ice cream cost a total
4).
Two bottles of root beer and a $3 ice cream cost a total
of $ How much is each bottle?
Picture
Equation =
2x =
5.40 ?
_________ =
5.40
2x =
5.40
5.40
= 2.70 2 =
2.70
x =
2.70

4. 5). What is x worth in the picture below?
Equation
91 =
5 + x
91 = x 86 ?
_________ 86 = x
86 = 4x 86
= 21.5 4
21.5
= x
21.5 = x

5. 2). Current Value Instructions Algebra Tiles 5 8 16 10 5 a).
Pick any number. x 5 8
b).
Now add 3.
c).
Multiply that answer by 2. 16
d).
Subtract 6 from that answer. 10
e).
Divide that answer by 2. 5

6. 2). Current Value Instructions Algebra Tiles 5 8 16 10 5 a).
Pick any number. x 5 x 1 1 1 8
b).
Now add 3.
c).
Multiply that answer by 2. 16
d).
Subtract 6 from that answer. 10
e).
Divide that answer by 2. 5

7. 2). Current Value Instructions Algebra Tiles 5 8 16 10 5 a).
Pick any number. 5 8
b).
Now add 3.
c).
Multiply that answer by 2. 16
d).
Subtract 6 from that answer. 10
e).
Divide that answer by 2. 5

8. 2). Current Value Instructions Algebra Tiles 5 8 16 10 5 a).
Pick any number. 5 8
b).
Now add 3.
c).
Multiply that answer by 2. 16
d).
Subtract 6 from that answer. 10
e).
Divide that answer by 2. 5

9. 2). Current Value Instructions Algebra Tiles 5 8 16 10 5 a).
Pick any number. 5 8
b).
Now add 3.
c).
Multiply that answer by 2. 16
d).
Subtract 6 from that answer. 10
e).
Divide that answer by 2. 5

10. Original number 2). Current Value Instructions Algebra Tiles 5 8 16 10
Pick any number. 5 8
b).
Now add 3.
Original number
c).
Multiply that answer by 2. 16
d).
Subtract 6 from that answer. 10
e).
Divide that answer by 2. 5
Final picture:

11. Keeping an Equation Balanced
Fill out this part of your handout as we go over it, please.

12. Keeping an Equation Balanced
“2 + 3 = 5” means that balances out with 5.
2 + 3 = 5

13. What will happen if we subtract something from ONLY this side?
Discussion
2 + 3 5 3
– 2

14. What will happen if we subtract something from ONLY this side?
2 + 3 3
What happens now?

15. What will happen if you subtract something from ONLY this side?3 3 3
2 + 3 3
2 + 3
2 + 3
2 + 3

16. 2 + 3 – 2 5 – 2 3 3 2 + 3 – 2 5 – 2 3 Do the same thing to both sides
to keep the equation balanced.
2 + 3
– 2 5
– 2 3 3
Scratch work
2 + 3
– 2 5
– 2 3

17. 2 rules to follow when solving equations
The goal is to…
To keep the equation balanced, you have to…

18. Let’s practice solving equations using algebra tiles.

19. 7). 2x = 9

20. 7). 2x = 9

21. 7). 2x = 9
Draw this on your handout

22. Draw this on your handout.
7). 2x = 9
Draw this on your handout.
Take away
Take away
What can you do to both sides that will get an x by itself?

23. 7). 2x = 9
Draw this on your handout

24. 7). 2x = 9
How much is each x worth?
x = 3

25. Always look at the original picture to check the answer.
7). 2x = 9
Let’s check our answer
x = 3 3
Always look at the original picture to check the answer. 3

26. 7). 2x = 9 3
Let’s check our answer 3
Total = ___

27. 7). 2x = 9 3
Let’s check our answer 3
Total = 9
Total = ___

28. 7). 2x = 9 3 3
Total = 9
Total = 9
What do you think would happen if you substitute any other value for x (instead of 3)?

29. Watch and discuss the steps of #8 so you can do #9 on your own.

30. 8).
x = x

31. 8). 1 + 4x = 7 + 3x Take away Take away
What can you do to both sides to get an x by itself?

32. 8). 1 + 4x = 7 + 3x Take away Take away
What can you do to both sides to get an x by itself?

33. 8).
x = x
x = 6
How much is each x worth?

34. Always to back to the original picture to check.
8).
x = x
Check your answer
x = 6
Always to back to the original picture to check.

35. The answer to the check step is part of your answer. Not optional!
8).
x = x
Check your answer
x = 6 6 6 6 6 6 6 6
Total =
___
1 + 24
Total =
___
7 + 18
Total = 25
Total = 25
The answer to the check step is part of your answer. Not optional!
25 = 25

37. 9).
x = x
What can you do to both sides to get an x by itself?

38. 9). 1 + 2x = 4x Take away Take away
What can you do to both sides to get an x by itself?

39. 9). 1 + 2x = 4x x = 0.5 x = half of 1 ?? Take away Take away
How much is each x worth?

40. Let’s check our answer 9). 1 + 2x = 4x Total = ___ 1 + 1 Total = ___ 2
0.5
0.5
0.5
0.5
Let’s check our answer
0.5
0.5
Total =
___
1 + 1
Total =
___ 2
x = 0.5
Total = 2
Check: 2 = 2

42. 10).
x = 2x

43. 10).
x = 2x
Take away
Take away
Take away
Take away

44. 10).
x = 2x
Take away
Take away
Take away
Take away
x = 4

45. Let’s check our answer 10). 2 + 5x = 2x + 14 Total = ___ 2+ 20 Total =
8 + 14
Total = 22
Total = 22
Check: 22 = 22
x = 4