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Section 0-6Linear Inequalities
Wednesday, September 14, 2011
Essential Question
• How do you use Algebra to solve linear inequalities?
Wednesday, September 14, 2011
Inequalities
Wednesday, September 14, 2011
Inequalities
• Still want to isolate variable
Wednesday, September 14, 2011
Inequalities
• Still want to isolate variable
• Follow opposite operations
Wednesday, September 14, 2011
Inequalities
• Still want to isolate variable
• Follow opposite operations
• <, >, ≤, ≥, ≠
Wednesday, September 14, 2011
Example 1Solve.
a. x +7 < 4 b. − 2a +12 ≥ 32
Wednesday, September 14, 2011
Example 1Solve.
a. x +7 < 4 b. − 2a +12 ≥ 32 −7 −7
Wednesday, September 14, 2011
Example 1Solve.
a. x +7 < 4 b. − 2a +12 ≥ 32 −7 −7
x < −3
Wednesday, September 14, 2011
Example 1Solve.
a. x +7 < 4 b. − 2a +12 ≥ 32 −7 −7
x < −3
x |x < −3{ }
Wednesday, September 14, 2011
Example 1Solve.
a. x +7 < 4 b. − 2a +12 ≥ 32 −7 −7
x < −3
x |x < −3{ }
−12 −12
Wednesday, September 14, 2011
Example 1Solve.
a. x +7 < 4 b. − 2a +12 ≥ 32 −7 −7
x < −3
x |x < −3{ }
−12 −12
−2a ≥ 20
Wednesday, September 14, 2011
Example 1Solve.
a. x +7 < 4 b. − 2a +12 ≥ 32 −7 −7
x < −3
x |x < −3{ }
−12 −12
−2a ≥ 20
a|a ≥ −10{ }
Wednesday, September 14, 2011
Example 1Solve.
a. x +7 < 4 b. − 2a +12 ≥ 32 −7 −7
x < −3
x |x < −3{ }
−12 −12
−2a ≥ 20
a|a ≥ −10{ } −2 −2
Wednesday, September 14, 2011
Example 1Solve.
c. 18t > 63 d. − f
7≤13
Wednesday, September 14, 2011
Example 1Solve.
c. 18t > 63 d. − f
7≤13
18 18
Wednesday, September 14, 2011
Example 1Solve.
c. 18t > 63 d. − f
7≤13
t|t >
72
⎧⎨⎩
⎫⎬⎭
18 18
Wednesday, September 14, 2011
Example 1Solve.
c. 18t > 63 d. − f
7≤13
t|t >
72
⎧⎨⎩
⎫⎬⎭
18 18
−7 −
f7
⎛⎝⎜
⎞⎠⎟≤13(−7)
Wednesday, September 14, 2011
Example 1Solve.
c. 18t > 63 d. − f
7≤13
t|t >
72
⎧⎨⎩
⎫⎬⎭
f |f ≥ −91{ }
18 18
−7 −
f7
⎛⎝⎜
⎞⎠⎟≤13(−7)
Wednesday, September 14, 2011
Example 1Solve.
e. 3
4k +9 ≠ 45 f. 3g − 24 ≥ 9g +12
Wednesday, September 14, 2011
Example 1Solve.
e. 3
4k +9 ≠ 45 f. 3g − 24 ≥ 9g +12
−9 −9
Wednesday, September 14, 2011
Example 1Solve.
e. 3
4k +9 ≠ 45 f. 3g − 24 ≥ 9g +12
−9 −9
34
k ≠ 36
Wednesday, September 14, 2011
Example 1Solve.
e. 3
4k +9 ≠ 45 f. 3g − 24 ≥ 9g +12
−9 −9
34
k ≠ 36 43
i i43
Wednesday, September 14, 2011
Example 1Solve.
e. 3
4k +9 ≠ 45 f. 3g − 24 ≥ 9g +12
−9 −9
34
k ≠ 36
k |k ≠ 48{ } 43
i i43
Wednesday, September 14, 2011
Example 1Solve.
e. 3
4k +9 ≠ 45 f. 3g − 24 ≥ 9g +12
−9 −9
34
k ≠ 36
k |k ≠ 48{ } 43
i i43
−12 −12 −3g −3g
Wednesday, September 14, 2011
Example 1Solve.
e. 3
4k +9 ≠ 45 f. 3g − 24 ≥ 9g +12
−9 −9
34
k ≠ 36
k |k ≠ 48{ }
−36 ≥ 6g 43
i i43
−12 −12 −3g −3g
Wednesday, September 14, 2011
Example 1Solve.
e. 3
4k +9 ≠ 45 f. 3g − 24 ≥ 9g +12
−9 −9
34
k ≠ 36
k |k ≠ 48{ }
−36 ≥ 6g 6 6
43
i i43
−12 −12 −3g −3g
Wednesday, September 14, 2011
Example 1Solve.
e. 3
4k +9 ≠ 45 f. 3g − 24 ≥ 9g +12
−9 −9
34
k ≠ 36
k |k ≠ 48{ }
−36 ≥ 6g
g |g ≤ −6{ } 6 6
43
i i43
−12 −12 −3g −3g
Wednesday, September 14, 2011
Problem Set
Wednesday, September 14, 2011
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. EdisonWednesday, September 14, 2011