geometry section 0-6 11-12

Section 0-6Linear Inequalities

Wednesday, September 14, 2011

Essential Question

• How do you use Algebra to solve linear inequalities?


Inequalities


Inequalities

• Still want to isolate variable


Inequalities


• Follow opposite operations


Inequalities


• Follow opposite operations

• <, >, ≤, ≥, ≠


Example 1Solve.

a. x +7 < 4 b. − 2a +12 ≥ 32


Example 1Solve.

a. x +7 < 4 b. − 2a +12 ≥ 32 −7 −7


Example 1Solve.

a. x +7 < 4 b. − 2a +12 ≥ 32 −7 −7

x < −3


Example 1Solve.

a. x +7 < 4 b. − 2a +12 ≥ 32 −7 −7

x < −3

x |x < −3{ }


Example 1Solve.

a. x +7 < 4 b. − 2a +12 ≥ 32 −7 −7

x < −3

x |x < −3{ }

−12 −12


Example 1Solve.

a. x +7 < 4 b. − 2a +12 ≥ 32 −7 −7

x < −3

x |x < −3{ }

−12 −12

−2a ≥ 20


Example 1Solve.

a. x +7 < 4 b. − 2a +12 ≥ 32 −7 −7

x < −3

x |x < −3{ }

−12 −12

−2a ≥ 20 −2 −2


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


Example 1Solve.

c. 18t > 63 d. − f

7≤13


Example 1Solve.

c. 18t > 63 d. − f

7≤13

18 18


Example 1Solve.

c. 18t > 63 d. − f

7≤13

t|t >

72

⎧⎨⎩

⎫⎬⎭

18 18


Example 1Solve.

c. 18t > 63 d. − f

7≤13

t|t >

72

⎧⎨⎩

⎫⎬⎭

18 18

−7 −

f7

⎛⎝⎜

⎞⎠⎟≤13(−7)


Example 1Solve.

c. 18t > 63 d. − f

7≤13

t|t >

72

⎧⎨⎩

⎫⎬⎭

f |f ≥ −91{ }

18 18

−7 −

f7

⎛⎝⎜

⎞⎠⎟≤13(−7)


Example 1Solve.

e. 3

4k +9 ≠ 45 f. 3g − 24 ≥ 9g +12


Example 1Solve.

e. 3

4k +9 ≠ 45 f. 3g − 24 ≥ 9g +12

−9 −9


Example 1Solve.

e. 3

4k +9 ≠ 45 f. 3g − 24 ≥ 9g +12

−9 −9

34

k ≠ 36


Example 1Solve.

e. 3

4k +9 ≠ 45 f. 3g − 24 ≥ 9g +12

−9 −9

34

k ≠ 36 43

i i43


Example 1Solve.

e. 3

4k +9 ≠ 45 f. 3g − 24 ≥ 9g +12

−9 −9

34

k ≠ 36

k |k ≠ 48{ } 43

i i43


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


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


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


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


Problem Set


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

geometry section 0-6 11-12

Education