More Related Content More from Jimbo Lamb (20) Recently uploaded Industrial Policy - 1948, 1956, 1973, 1977, 1980, 1991 Industrial Policy - 1948, 1956, 1973, 1977, 1980, 1991 RKavithamani
1. Section 0-6
Linear Inequalities
Wednesday, September 14, 2011
2. Essential Question
• How do you use Algebra to solve linear
inequalities?
Wednesday, September 14, 2011
4. Inequalities
• Still want to isolate variable
Wednesday, September 14, 2011
5. Inequalities
• Still want to isolate variable
• Follow opposite operations
Wednesday, September 14, 2011
6. Inequalities
• Still want to isolate variable
• Follow opposite operations
• <, >, ≤, ≥, ≠
Wednesday, September 14, 2011
7. Example 1
Solve.
a. x + 7 < 4 b. − 2a + 12 ≥ 32
Wednesday, September 14, 2011
8. Example 1
Solve.
a. x + 7 < 4 b. − 2a + 12 ≥ 32
−7 −7
Wednesday, September 14, 2011
9. Example 1
Solve.
a. x + 7 < 4 b. − 2a + 12 ≥ 32
−7 −7
x < −3
Wednesday, September 14, 2011
10. Example 1
Solve.
a. x + 7 < 4 b. − 2a + 12 ≥ 32
−7 −7
x < −3
{x | x < −3}
Wednesday, September 14, 2011
11. Example 1
Solve.
a. x + 7 < 4 b. − 2a + 12 ≥ 32
−7 −7 −12 −12
x < −3
{x | x < −3}
Wednesday, September 14, 2011
12. Example 1
Solve.
a. x + 7 < 4 b. − 2a + 12 ≥ 32
−7 −7 −12 −12
x < −3 −2a ≥ 20
{x | x < −3}
Wednesday, September 14, 2011
13. Example 1
Solve.
a. x + 7 < 4 b. − 2a + 12 ≥ 32
−7 −7 −12 −12
x < −3 −2a ≥ 20
{x | x < −3} −2 −2
Wednesday, September 14, 2011
14. Example 1
Solve.
a. x + 7 < 4 b. − 2a + 12 ≥ 32
−7 −7 −12 −12
x < −3 −2a ≥ 20
{x | x < −3} −2 −2
{a |a ≤ −10}
Wednesday, September 14, 2011
15. Example 1
Solve.
f
c. 18t > 63 d. − ≤ 13
7
Wednesday, September 14, 2011
16. Example 1
Solve.
f
c. 18t > 63 d. − ≤ 13
18 18 7
Wednesday, September 14, 2011
17. Example 1
Solve.
f
c. 18t > 63 d. − ≤ 13
18 18 7
⎧ 7⎫
⎨t |t > ⎬
⎩ 2⎭
Wednesday, September 14, 2011
18. Example 1
Solve.
f
c. 18t > 63 d. − ≤ 13
18 18 7
⎛ f⎞
⎧ 7⎫ −7 ⎜ − ⎟ ≤ 13(−7)
⎨t |t > ⎬ ⎝ 7⎠
⎩ 2⎭
Wednesday, September 14, 2011
19. Example 1
Solve.
f
c. 18t > 63 d. − ≤ 13
18 18 7
⎛ f⎞
⎧ 7⎫ −7 ⎜ − ⎟ ≤ 13(−7)
⎨t |t > ⎬ ⎝ 7⎠
⎩ 2⎭
{f | f ≥ −91}
Wednesday, September 14, 2011
20. Example 1
Solve.
3
e. k + 9 ≠ 45 f. 3g − 24 ≥ 9g + 12
4
Wednesday, September 14, 2011
21. Example 1
Solve.
3
e. k + 9 ≠ 45 f. 3g − 24 ≥ 9g + 12
4 −9 −9
Wednesday, September 14, 2011
22. Example 1
Solve.
3
e. k + 9 ≠ 45 f. 3g − 24 ≥ 9g + 12
4 −9 −9
3
k ≠ 36
4
Wednesday, September 14, 2011
23. Example 1
Solve.
3
e. k + 9 ≠ 45 f. 3g − 24 ≥ 9g + 12
4 −9 −9
4 3 4
i k ≠ 36 i
3 4 3
Wednesday, September 14, 2011
24. Example 1
Solve.
3
e. k + 9 ≠ 45 f. 3g − 24 ≥ 9g + 12
4 −9 −9
4 3 4
i k ≠ 36 i
3 4 3
{k | k ≠ 48}
Wednesday, September 14, 2011
25. Example 1
Solve.
3
e. k + 9 ≠ 45 f. 3g − 24 ≥ 9g + 12
4 −9 −9 −3g −12 −3g −12
4 3 4
i k ≠ 36 i
3 4 3
{k | k ≠ 48}
Wednesday, September 14, 2011
26. Example 1
Solve.
3
e. k + 9 ≠ 45 f. 3g − 24 ≥ 9g + 12
4 −9 −9 −3g −12 −3g −12
4 3 4 −36 ≥ 6g
i k ≠ 36 i
3 4 3
{k | k ≠ 48}
Wednesday, September 14, 2011
27. Example 1
Solve.
3
e. k + 9 ≠ 45 f. 3g − 24 ≥ 9g + 12
4 −9 −9 −3g −12 −3g −12
4 3 4 −36 ≥ 6g
i k ≠ 36 i
3 4 3 6 6
{k | k ≠ 48}
Wednesday, September 14, 2011
28. Example 1
Solve.
3
e. k + 9 ≠ 45 f. 3g − 24 ≥ 9g + 12
4 −9 −9 −3g −12 −3g −12
4 3 4 −36 ≥ 6g
i k ≠ 36 i
3 4 3 6 6
{k | k ≠ 48} {g | g ≤ −6}
Wednesday, September 14, 2011
30. Problem Set
p. P14 #1-23 odd
“Opportunity is missed by most people because it
is dressed in overalls and looks like work.”
- Thomas A. Edison
Wednesday, September 14, 2011
