Weitere ähnliche Inhalte Kürzlich hochgeladen (20) 1. Section 0-5
Linear Equations
Wednesday, September 14, 2011
2. Essential Question
• How do you use Algebra to solve linear
equations?
Wednesday, September 14, 2011
5. Things to Remember
• Isolate the variable
• Do the opposite operations
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6. Things to Remember
• Isolate the variable
• Do the opposite operations
• Check your answers
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7. Example 1
Solve.
a. x −18 = −4 b. 2b +12 = 20
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8. Example 1
Solve.
a. x −18 = −4 b. 2b +12 = 20
+18
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9. Example 1
Solve.
a. x −18 = −4 b. 2b +12 = 20
+18 +18
Wednesday, September 14, 2011
10. Example 1
Solve.
a. x −18 = −4 b. 2b +12 = 20
+18 +18
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11. Example 1
Solve.
a. x −18 = −4 b. 2b +12 = 20
+18 +18
x =14
Wednesday, September 14, 2011
12. Example 1
Solve.
a. x −18 = −4 b. 2b +12 = 20
+18 +18
x =14
Check:
Wednesday, September 14, 2011
13. Example 1
Solve.
a. x −18 = −4 b. 2b +12 = 20
+18 +18
x =14
Check:
14 −18 = −4
Wednesday, September 14, 2011
14. Example 1
Solve.
a. x −18 = −4 b. 2b +12 = 20
+18 +18 −12
x =14
Check:
14 −18 = −4
Wednesday, September 14, 2011
15. Example 1
Solve.
a. x −18 = −4 b. 2b +12 = 20
+18 +18 −12 −12
x =14
Check:
14 −18 = −4
Wednesday, September 14, 2011
16. Example 1
Solve.
a. x −18 = −4 b. 2b +12 = 20
+18 +18 −12 −12
x =14
Check:
14 −18 = −4
Wednesday, September 14, 2011
17. Example 1
Solve.
a. x −18 = −4 b. 2b +12 = 20
+18 +18 −12 −12
x =14 2b = 8
Check:
14 −18 = −4
Wednesday, September 14, 2011
18. Example 1
Solve.
a. x −18 = −4 b. 2b +12 = 20
+18 +18 −12 −12
x =14 2b = 8
2
Check:
14 −18 = −4
Wednesday, September 14, 2011
19. Example 1
Solve.
a. x −18 = −4 b. 2b +12 = 20
+18 +18 −12 −12
x =14 2b = 8
2 2
Check:
14 −18 = −4
Wednesday, September 14, 2011
20. Example 1
Solve.
a. x −18 = −4 b. 2b +12 = 20
+18 +18 −12 −12
x =14 2b = 8
2 2
Check:
b=4
14 −18 = −4
Wednesday, September 14, 2011
21. Example 1
Solve.
a. x −18 = −4 b. 2b +12 = 20
+18 +18 −12 −12
x =14 2b = 8
2 2
Check:
b=4
14 −18 = −4
Check:
Wednesday, September 14, 2011
22. Example 1
Solve.
a. x −18 = −4 b. 2b +12 = 20
+18 +18 −12 −12
x =14 2b = 8
2 2
Check:
b=4
14 −18 = −4
Check:
2(4) +12 = 20
Wednesday, September 14, 2011
23. Example 1
Solve.
a. x −18 = −4 b. 2b +12 = 20
+18 +18 −12 −12
x =14 2b = 8
2 2
Check:
b=4
14 −18 = −4
Check:
2(4) +12 = 20
8 +12 = 20
Wednesday, September 14, 2011
24. Example 1
Solve.
c. 5t =125 r
d. − = 5
6
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25. Example 1
Solve.
c. 5t =125 r
5 d. − = 5
6
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26. Example 1
Solve.
c. 5t =125 r
5 5 d. − = 5
6
Wednesday, September 14, 2011
27. Example 1
Solve.
c. 5t =125 r
5 5 d. − = 5
6
t = 25
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28. Example 1
Solve.
c. 5t =125 r
5 5 d. − = 5
6
t = 25
Check:
Wednesday, September 14, 2011
29. Example 1
Solve.
c. 5t =125 r
5 5 d. − = 5
6
t = 25
Check:
5(25) =125
Wednesday, September 14, 2011
30. Example 1
Solve.
c. 5t =125 r
5 5 d. − = 5
6
t = 25 r
(−6)(− ) = 5(−6)
Check: 6
5(25) =125
Wednesday, September 14, 2011
31. Example 1
Solve.
c. 5t =125 r
5 5 d. − = 5
6
t = 25 r
(−6)(− ) = 5(−6)
Check: 6
r = −30
5(25) =125
Wednesday, September 14, 2011
32. Example 1
Solve.
c. 5t =125 r
5 5 d. − = 5
6
t = 25 r
(−6)(− ) = 5(−6)
Check: 6
r = −30
5(25) =125 Check:
Wednesday, September 14, 2011
33. Example 1
Solve.
c. 5t =125 r
5 5 d. − = 5
6
t = 25 r
(−6)(− ) = 5(−6)
Check: 6
r = −30
5(25) =125 Check:
−30
− =5
6
Wednesday, September 14, 2011
34. Example 1
Solve.
2
e. h + 9 =17
3
Wednesday, September 14, 2011
35. Example 1
Solve.
2
e. h + 9 =17
3 −9
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36. Example 1
Solve.
2
e. h + 9 =17
3 −9 −9
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37. Example 1
Solve.
2
e. h + 9 =17
3 −9 −9
Wednesday, September 14, 2011
38. Example 1
Solve.
2
e. h + 9 =17
3 −9 −9
2
h=8
3
Wednesday, September 14, 2011
39. Example 1
Solve.
2
e. h + 9 =17
3 −9 −9
2
h=8
3
⎛ 3⎞ ⎛ 2 ⎞ ⎛ 3⎞
h⎟ = 8 ⎜ ⎟
⎜ 2⎟ ⎜ 3 ⎠
⎝ ⎠⎝ ⎝ 2⎠
Wednesday, September 14, 2011
40. Example 1
Solve.
2
e. h + 9 =17
3 −9 −9 h =12
2
h=8
3
⎛ 3⎞ ⎛ 2 ⎞ ⎛ 3⎞
h⎟ = 8 ⎜ ⎟
⎜ 2⎟ ⎜ 3 ⎠
⎝ ⎠⎝ ⎝ 2⎠
Wednesday, September 14, 2011
41. Example 1
Solve.
2
e. h + 9 =17
3 −9 −9 h =12
2 Check:
h=8
3
⎛ 3⎞ ⎛ 2 ⎞ ⎛ 3⎞
h⎟ = 8 ⎜ ⎟
⎜ 2⎟ ⎜ 3 ⎠
⎝ ⎠⎝ ⎝ 2⎠
Wednesday, September 14, 2011
42. Example 1
Solve.
2
e. h + 9 =17
3 −9 −9 h =12
2 Check:
h=8
3 2
(12) + 9 =17
⎛ 3⎞ ⎛ 2 ⎞ ⎛ 3⎞ 3
h⎟ = 8 ⎜ ⎟
⎜ 2⎟ ⎜ 3 ⎠
⎝ ⎠⎝ ⎝ 2⎠
Wednesday, September 14, 2011
43. Example 1
Solve.
2
e. h + 9 =17
3 −9 −9 h =12
2 Check:
h=8
3 2
(12) + 9 =17
⎛ 3⎞ ⎛ 2 ⎞ ⎛ 3⎞ 3
h⎟ = 8 ⎜ ⎟
⎜ 2⎟ ⎜ 3 ⎠
⎝ ⎠⎝ ⎝ 2⎠ 8 + 9 =17
Wednesday, September 14, 2011
44. Example 1
Solve.
f. 4m − 3 = 7m +12
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45. Example 1
Solve.
f. 4m − 3 = 7m +12
−4m −4m
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46. Example 1
Solve.
f. 4m − 3 = 7m +12
−4m −12 −4m −12
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47. Example 1
Solve.
f. 4m − 3 = 7m +12
−4m −12 −4m −12
−15 = 3m
Wednesday, September 14, 2011
48. Example 1
Solve.
f. 4m − 3 = 7m +12
−4m −12 −4m −12
−15 = 3m
3
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49. Example 1
Solve.
f. 4m − 3 = 7m +12
−4m −12 −4m −12
−15 = 3m
3 3
Wednesday, September 14, 2011
50. Example 1
Solve.
f. 4m − 3 = 7m +12
−4m −12 −4m −12
−15 = 3m
3 3
−5 = m
Wednesday, September 14, 2011
51. Example 1
Solve.
f. 4m − 3 = 7m +12
−4m −12 −4m −12 Check:
−15 = 3m
3 3
−5 = m
Wednesday, September 14, 2011
52. Example 1
Solve.
f. 4m − 3 = 7m +12
−4m −12 −4m −12 Check:
−15 = 3m 4(−5) − 3 = 7(−5) +12
3 3
−5 = m
Wednesday, September 14, 2011
53. Example 1
Solve.
f. 4m − 3 = 7m +12
−4m −12 −4m −12 Check:
−15 = 3m 4(−5) − 3 = 7(−5) +12
3 3
−20 − 3 = −35 +12
−5 = m
Wednesday, September 14, 2011
54. Example 1
Solve.
f. 4m − 3 = 7m +12
−4m −12 −4m −12 Check:
−15 = 3m 4(−5) − 3 = 7(−5) +12
3 3
−20 − 3 = −35 +12
−5 = m −23 = −23
Wednesday, September 14, 2011
56. Problem Set
p. P12 #1-36, multiples of 3
“When you make a mistake, there are only three things you
should ever do about it: admit it, learns from it, and don’t
repeat it.” - Paul “Bear” Bryant
Wednesday, September 14, 2011
