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A.8 Interval Notation & Solving Inequalitie s Remember, with great power, comes great responsibility. -Uncle Ben

A.8 Interval Notation Solving Inequalities Remember, with great power, comes great responsibility. -Uncle Ben

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Write the following inequalities in interval notation and graph on a number line. Interval Notation 1) 2) 3) 4)

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Page 1: A.8 Interval Notation  Solving Inequalities Remember, with great power, comes great responsibility. -Uncle Ben

A.8 Interval Notation &

Solving Inequalities

Remember, with great power, comes great responsibility.-Uncle Ben

Page 2: A.8 Interval Notation  Solving Inequalities Remember, with great power, comes great responsibility. -Uncle Ben

Interval Notation

: A closed interval consists of all real x such that

[a,b]

ax b

: An open interval consists of all real x such that

(a,b)

a x b

A half-open or half-closed interval consists of all real x such

that

[a,b)

ax b

(a,b]

a x b:

x a

[a,) : The interval

(a,)

x a: The interval

x a

( ,a] : The interval

( ,a)

x a: The interval

Page 3: A.8 Interval Notation  Solving Inequalities Remember, with great power, comes great responsibility. -Uncle Ben

Write the following inequalities in interval notation and graph on a number line.

Interval Notation

2x 4

3x 8

x 1

x 5

1)

2)

3)

4)

Page 4: A.8 Interval Notation  Solving Inequalities Remember, with great power, comes great responsibility. -Uncle Ben

Solving Linear Inequalities

Recall that when you multiply or divide by a negative number, you must change the direction of the inequality.

8 3(2 x) 2x1)

Page 5: A.8 Interval Notation  Solving Inequalities Remember, with great power, comes great responsibility. -Uncle Ben

Linear Inequalities Practice

Solve the following inequality. Write your answer in interval notation and graph on a number line.

4x 72x 3

3)

5 3x 2 1

13 3x 7 5

14

2x 32

52

4)

1)

2)

Page 6: A.8 Interval Notation  Solving Inequalities Remember, with great power, comes great responsibility. -Uncle Ben

Solving Absolute Value Inequalities

u a

aua

x 3

0 1 2 3 4 5 6-2 -1-4 -3-6 -5

Remember: Less ThAND

Page 7: A.8 Interval Notation  Solving Inequalities Remember, with great power, comes great responsibility. -Uncle Ben

Solving Absolute Value Inequalities

u a

ua or u a

x 3

0 1 2 3 4 5 6-2 -1-4 -3-6 -5

Remember: GreatOR

Page 8: A.8 Interval Notation  Solving Inequalities Remember, with great power, comes great responsibility. -Uncle Ben

Solving Absolute Value Inequalities

2 3x 5 13

0 1 2 3 4 5 6-2 -1-4 -3-6 -5

Page 9: A.8 Interval Notation  Solving Inequalities Remember, with great power, comes great responsibility. -Uncle Ben

Solving Absolute Value Inequalities

1 2x 24

0 1 2 3 4 5 6-2 -1-4 -3-6 -5

Page 10: A.8 Interval Notation  Solving Inequalities Remember, with great power, comes great responsibility. -Uncle Ben

More Practice

2 2x 5 151)

0 1 2 3 4 5 6-2 -1-4 -3-6 -5

Page 11: A.8 Interval Notation  Solving Inequalities Remember, with great power, comes great responsibility. -Uncle Ben

More Practice

2 3x 4 22)

0 1 2 3 4 5 6-2 -1-4 -3-6 -5

Page 12: A.8 Interval Notation  Solving Inequalities Remember, with great power, comes great responsibility. -Uncle Ben

You guys should try some before I give you the HW, k?Solve, write your answer in interval notation, and graph!

Absolute Value Inequality Practice

4 2x 4 7

2x 5 7 4

4 3x 310

1)

2)

3)

Page 13: A.8 Interval Notation  Solving Inequalities Remember, with great power, comes great responsibility. -Uncle Ben

A.8 Interval Notation &

Solving Inequalities

Remember, with great power, comes great responsibility.-Uncle Ben

Homework#10 : p.1030

#77 – 99 Odd