A.8 Interval Notation Solving Inequalities Remember, with great power, comes great responsibility....
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Transcript of A.8 Interval Notation Solving Inequalities Remember, with great power, comes great responsibility....
![Page 1: A.8 Interval Notation Solving Inequalities Remember, with great power, comes great responsibility. -Uncle Ben.](https://reader035.fdocuments.us/reader035/viewer/2022070607/5a4d1b917f8b9ab0599c11fd/html5/thumbnails/1.jpg)
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.](https://reader035.fdocuments.us/reader035/viewer/2022070607/5a4d1b917f8b9ab0599c11fd/html5/thumbnails/2.jpg)
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.](https://reader035.fdocuments.us/reader035/viewer/2022070607/5a4d1b917f8b9ab0599c11fd/html5/thumbnails/3.jpg)
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.](https://reader035.fdocuments.us/reader035/viewer/2022070607/5a4d1b917f8b9ab0599c11fd/html5/thumbnails/4.jpg)
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.](https://reader035.fdocuments.us/reader035/viewer/2022070607/5a4d1b917f8b9ab0599c11fd/html5/thumbnails/5.jpg)
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.](https://reader035.fdocuments.us/reader035/viewer/2022070607/5a4d1b917f8b9ab0599c11fd/html5/thumbnails/6.jpg)
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.](https://reader035.fdocuments.us/reader035/viewer/2022070607/5a4d1b917f8b9ab0599c11fd/html5/thumbnails/7.jpg)
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.](https://reader035.fdocuments.us/reader035/viewer/2022070607/5a4d1b917f8b9ab0599c11fd/html5/thumbnails/8.jpg)
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.](https://reader035.fdocuments.us/reader035/viewer/2022070607/5a4d1b917f8b9ab0599c11fd/html5/thumbnails/9.jpg)
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.](https://reader035.fdocuments.us/reader035/viewer/2022070607/5a4d1b917f8b9ab0599c11fd/html5/thumbnails/10.jpg)
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.](https://reader035.fdocuments.us/reader035/viewer/2022070607/5a4d1b917f8b9ab0599c11fd/html5/thumbnails/11.jpg)
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.](https://reader035.fdocuments.us/reader035/viewer/2022070607/5a4d1b917f8b9ab0599c11fd/html5/thumbnails/12.jpg)
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.](https://reader035.fdocuments.us/reader035/viewer/2022070607/5a4d1b917f8b9ab0599c11fd/html5/thumbnails/13.jpg)
A.8 Interval Notation &
Solving Inequalities
Remember, with great power, comes great responsibility.-Uncle Ben
Homework#10 : p.1030
#77 – 99 Odd