4x 3 9 and 2 5x < 7 - university of alaska...
TRANSCRIPT
![Page 1: 4x 3 9 and 2 5x < 7 - University of Alaska Anchoragemath.uaa.alaska.edu/~afmaf/classes/math105/notes/...Solving Inequalities by Inversion Keywords: equation, solve, solving, inversion](https://reader033.vdocument.in/reader033/viewer/2022050303/5f6bde83ec36804e14223878/html5/thumbnails/1.jpg)
Multiple Inequalities
4x− 3 < 9, and 2− 5x < 7.
![Page 2: 4x 3 9 and 2 5x < 7 - University of Alaska Anchoragemath.uaa.alaska.edu/~afmaf/classes/math105/notes/...Solving Inequalities by Inversion Keywords: equation, solve, solving, inversion](https://reader033.vdocument.in/reader033/viewer/2022050303/5f6bde83ec36804e14223878/html5/thumbnails/2.jpg)
Multiple Inequalities
4x− 3 < 9, and 2− 5x < 7.4x < 12,
![Page 3: 4x 3 9 and 2 5x < 7 - University of Alaska Anchoragemath.uaa.alaska.edu/~afmaf/classes/math105/notes/...Solving Inequalities by Inversion Keywords: equation, solve, solving, inversion](https://reader033.vdocument.in/reader033/viewer/2022050303/5f6bde83ec36804e14223878/html5/thumbnails/3.jpg)
Multiple Inequalities
4x− 3 < 9, and 2− 5x < 7.4x < 12,x < 3,
![Page 4: 4x 3 9 and 2 5x < 7 - University of Alaska Anchoragemath.uaa.alaska.edu/~afmaf/classes/math105/notes/...Solving Inequalities by Inversion Keywords: equation, solve, solving, inversion](https://reader033.vdocument.in/reader033/viewer/2022050303/5f6bde83ec36804e14223878/html5/thumbnails/4.jpg)
Multiple Inequalities
4x− 3 < 9, and 2− 5x < 7.4x < 12, and −5x < 5.x < 3,
![Page 5: 4x 3 9 and 2 5x < 7 - University of Alaska Anchoragemath.uaa.alaska.edu/~afmaf/classes/math105/notes/...Solving Inequalities by Inversion Keywords: equation, solve, solving, inversion](https://reader033.vdocument.in/reader033/viewer/2022050303/5f6bde83ec36804e14223878/html5/thumbnails/5.jpg)
Multiple Inequalities
4x− 3 < 9, and 2− 5x < 7.4x < 12, and −5x < 5.x < 3, and x > −1.
![Page 6: 4x 3 9 and 2 5x < 7 - University of Alaska Anchoragemath.uaa.alaska.edu/~afmaf/classes/math105/notes/...Solving Inequalities by Inversion Keywords: equation, solve, solving, inversion](https://reader033.vdocument.in/reader033/viewer/2022050303/5f6bde83ec36804e14223878/html5/thumbnails/6.jpg)
Multiple Inequalities
4x− 3 < 9, and 2− 5x < 7.4x < 12, and −5x < 5.x < 3, and x > −1.
Graph x < 3
-2 -1 0 1 2 3 4
![Page 7: 4x 3 9 and 2 5x < 7 - University of Alaska Anchoragemath.uaa.alaska.edu/~afmaf/classes/math105/notes/...Solving Inequalities by Inversion Keywords: equation, solve, solving, inversion](https://reader033.vdocument.in/reader033/viewer/2022050303/5f6bde83ec36804e14223878/html5/thumbnails/7.jpg)
Multiple Inequalities
4x− 3 < 9, and 2− 5x < 7.4x < 12, and −5x < 5.x < 3, and x > −1.
Graph x > −1
-2 -1 0 1 2 3 4
![Page 8: 4x 3 9 and 2 5x < 7 - University of Alaska Anchoragemath.uaa.alaska.edu/~afmaf/classes/math105/notes/...Solving Inequalities by Inversion Keywords: equation, solve, solving, inversion](https://reader033.vdocument.in/reader033/viewer/2022050303/5f6bde83ec36804e14223878/html5/thumbnails/8.jpg)
Multiple Inequalities
4x− 3 < 9, and 2− 5x < 7.4x < 12, and −5x < 5.x < 3, and x > −1.
Graph the portion under both.
-2 -1 0 1 2 3 4
![Page 9: 4x 3 9 and 2 5x < 7 - University of Alaska Anchoragemath.uaa.alaska.edu/~afmaf/classes/math105/notes/...Solving Inequalities by Inversion Keywords: equation, solve, solving, inversion](https://reader033.vdocument.in/reader033/viewer/2022050303/5f6bde83ec36804e14223878/html5/thumbnails/9.jpg)
Multiple Inequalities
4x− 3 < 9, and 2− 5x < 7.4x < 12, and −5x < 5.x < 3, and x > −1.
-2 -1 0 1 2 3 4
What is the left endpoint?
( )
![Page 10: 4x 3 9 and 2 5x < 7 - University of Alaska Anchoragemath.uaa.alaska.edu/~afmaf/classes/math105/notes/...Solving Inequalities by Inversion Keywords: equation, solve, solving, inversion](https://reader033.vdocument.in/reader033/viewer/2022050303/5f6bde83ec36804e14223878/html5/thumbnails/10.jpg)
Multiple Inequalities
4x− 3 < 9, and 2− 5x < 7.4x < 12, and −5x < 5.x < 3, and x > −1.
-2 -1 0 1 2 3 4
What is the left endpoint? -1
(− 1, )
![Page 11: 4x 3 9 and 2 5x < 7 - University of Alaska Anchoragemath.uaa.alaska.edu/~afmaf/classes/math105/notes/...Solving Inequalities by Inversion Keywords: equation, solve, solving, inversion](https://reader033.vdocument.in/reader033/viewer/2022050303/5f6bde83ec36804e14223878/html5/thumbnails/11.jpg)
Multiple Inequalities
4x− 3 < 9, and 2− 5x < 7.4x < 12, and −5x < 5.x < 3, and x > −1.
-2 -1 0 1 2 3 4
What is the right endpoint?
(− 1, )
![Page 12: 4x 3 9 and 2 5x < 7 - University of Alaska Anchoragemath.uaa.alaska.edu/~afmaf/classes/math105/notes/...Solving Inequalities by Inversion Keywords: equation, solve, solving, inversion](https://reader033.vdocument.in/reader033/viewer/2022050303/5f6bde83ec36804e14223878/html5/thumbnails/12.jpg)
Multiple Inequalities
4x− 3 < 9, and 2− 5x < 7.4x < 12, and −5x < 5.x < 3, and x > −1.
-2 -1 0 1 2 3 4
What is the right endpoint? 3
(− 1, 3)
![Page 13: 4x 3 9 and 2 5x < 7 - University of Alaska Anchoragemath.uaa.alaska.edu/~afmaf/classes/math105/notes/...Solving Inequalities by Inversion Keywords: equation, solve, solving, inversion](https://reader033.vdocument.in/reader033/viewer/2022050303/5f6bde83ec36804e14223878/html5/thumbnails/13.jpg)
Multiple Inequalities
11− 7x > 60, and 3x− 11 < 1.
![Page 14: 4x 3 9 and 2 5x < 7 - University of Alaska Anchoragemath.uaa.alaska.edu/~afmaf/classes/math105/notes/...Solving Inequalities by Inversion Keywords: equation, solve, solving, inversion](https://reader033.vdocument.in/reader033/viewer/2022050303/5f6bde83ec36804e14223878/html5/thumbnails/14.jpg)
Multiple Inequalities
11− 7x > 60, and 3x− 11 < 1.−7x > 49,
![Page 15: 4x 3 9 and 2 5x < 7 - University of Alaska Anchoragemath.uaa.alaska.edu/~afmaf/classes/math105/notes/...Solving Inequalities by Inversion Keywords: equation, solve, solving, inversion](https://reader033.vdocument.in/reader033/viewer/2022050303/5f6bde83ec36804e14223878/html5/thumbnails/15.jpg)
Multiple Inequalities
11− 7x > 60, and 3x− 11 < 1.−7x > 49,x < −7,
![Page 16: 4x 3 9 and 2 5x < 7 - University of Alaska Anchoragemath.uaa.alaska.edu/~afmaf/classes/math105/notes/...Solving Inequalities by Inversion Keywords: equation, solve, solving, inversion](https://reader033.vdocument.in/reader033/viewer/2022050303/5f6bde83ec36804e14223878/html5/thumbnails/16.jpg)
Multiple Inequalities
11− 7x > 60, and 3x− 11 < 1.−7x > 49, and 3x < 12.x < −7,
![Page 17: 4x 3 9 and 2 5x < 7 - University of Alaska Anchoragemath.uaa.alaska.edu/~afmaf/classes/math105/notes/...Solving Inequalities by Inversion Keywords: equation, solve, solving, inversion](https://reader033.vdocument.in/reader033/viewer/2022050303/5f6bde83ec36804e14223878/html5/thumbnails/17.jpg)
Multiple Inequalities
11− 7x > 60, and 3x− 11 < 1.−7x > 49, and 3x < 12.x < −7, and x > 4.
![Page 18: 4x 3 9 and 2 5x < 7 - University of Alaska Anchoragemath.uaa.alaska.edu/~afmaf/classes/math105/notes/...Solving Inequalities by Inversion Keywords: equation, solve, solving, inversion](https://reader033.vdocument.in/reader033/viewer/2022050303/5f6bde83ec36804e14223878/html5/thumbnails/18.jpg)
Multiple Inequalities
11− 7x > 60, and 3x− 11 < 1.−7x > 49, and 3x < 12.x < −7, and x > 4.
Graph x < −7
-10 -7.5 -5 -2.5 0 2.5 5 7.5
![Page 19: 4x 3 9 and 2 5x < 7 - University of Alaska Anchoragemath.uaa.alaska.edu/~afmaf/classes/math105/notes/...Solving Inequalities by Inversion Keywords: equation, solve, solving, inversion](https://reader033.vdocument.in/reader033/viewer/2022050303/5f6bde83ec36804e14223878/html5/thumbnails/19.jpg)
Multiple Inequalities
11− 7x > 60, and 3x− 11 < 1.−7x > 49, and 3x < 12.x < −7, and x > 4.
Graph x > 4
-10 -7.5 -5 -2.5 0 2.5 5 7.5
![Page 20: 4x 3 9 and 2 5x < 7 - University of Alaska Anchoragemath.uaa.alaska.edu/~afmaf/classes/math105/notes/...Solving Inequalities by Inversion Keywords: equation, solve, solving, inversion](https://reader033.vdocument.in/reader033/viewer/2022050303/5f6bde83ec36804e14223878/html5/thumbnails/20.jpg)
Multiple Inequalities
11− 7x > 60, and 3x− 11 < 1.−7x > 49, and 3x < 12.x < −7, and x > 4.
Graph the portion under either.
-10 -7.5 -5 -2.5 0 2.5 5 7.5
![Page 21: 4x 3 9 and 2 5x < 7 - University of Alaska Anchoragemath.uaa.alaska.edu/~afmaf/classes/math105/notes/...Solving Inequalities by Inversion Keywords: equation, solve, solving, inversion](https://reader033.vdocument.in/reader033/viewer/2022050303/5f6bde83ec36804e14223878/html5/thumbnails/21.jpg)
Multiple Inequalities
11− 7x > 60, and 3x− 11 < 1.−7x > 49, and 3x < 12.x < −7, and x > 4.
-10 -7.5 -5 -2.5 0 2.5 5 7.5
What is the left endpoint?
( )
![Page 22: 4x 3 9 and 2 5x < 7 - University of Alaska Anchoragemath.uaa.alaska.edu/~afmaf/classes/math105/notes/...Solving Inequalities by Inversion Keywords: equation, solve, solving, inversion](https://reader033.vdocument.in/reader033/viewer/2022050303/5f6bde83ec36804e14223878/html5/thumbnails/22.jpg)
Multiple Inequalities
11− 7x > 60, and 3x− 11 < 1.−7x > 49, and 3x < 12.x < −7, and x > 4.
-10 -7.5 -5 -2.5 0 2.5 5 7.5
What is the left endpoint? There is none.
(−∞, )
![Page 23: 4x 3 9 and 2 5x < 7 - University of Alaska Anchoragemath.uaa.alaska.edu/~afmaf/classes/math105/notes/...Solving Inequalities by Inversion Keywords: equation, solve, solving, inversion](https://reader033.vdocument.in/reader033/viewer/2022050303/5f6bde83ec36804e14223878/html5/thumbnails/23.jpg)
Multiple Inequalities
11− 7x > 60, and 3x− 11 < 1.−7x > 49, and 3x < 12.x < −7, and x > 4.
-10 -7.5 -5 -2.5 0 2.5 5 7.5
What is the right endpoint?
(−∞, )
![Page 24: 4x 3 9 and 2 5x < 7 - University of Alaska Anchoragemath.uaa.alaska.edu/~afmaf/classes/math105/notes/...Solving Inequalities by Inversion Keywords: equation, solve, solving, inversion](https://reader033.vdocument.in/reader033/viewer/2022050303/5f6bde83ec36804e14223878/html5/thumbnails/24.jpg)
Multiple Inequalities
11− 7x > 60, and 3x− 11 < 1.−7x > 49, and 3x < 12.x < −7, and x > 4.
-10 -7.5 -5 -2.5 0 2.5 5 7.5
What is the right endpoint? -7
(−∞, − 7)
![Page 25: 4x 3 9 and 2 5x < 7 - University of Alaska Anchoragemath.uaa.alaska.edu/~afmaf/classes/math105/notes/...Solving Inequalities by Inversion Keywords: equation, solve, solving, inversion](https://reader033.vdocument.in/reader033/viewer/2022050303/5f6bde83ec36804e14223878/html5/thumbnails/25.jpg)
Multiple Inequalities
11− 7x > 60, and 3x− 11 < 1.−7x > 49, and 3x < 12.x < −7, and x > 4.
-10 -7.5 -5 -2.5 0 2.5 5 7.5
What is the left endpoint?
(−∞, − 7) ∪ ( )
![Page 26: 4x 3 9 and 2 5x < 7 - University of Alaska Anchoragemath.uaa.alaska.edu/~afmaf/classes/math105/notes/...Solving Inequalities by Inversion Keywords: equation, solve, solving, inversion](https://reader033.vdocument.in/reader033/viewer/2022050303/5f6bde83ec36804e14223878/html5/thumbnails/26.jpg)
Multiple Inequalities
11− 7x > 60, and 3x− 11 < 1.−7x > 49, and 3x < 12.x < −7, and x > 4.
-10 -7.5 -5 -2.5 0 2.5 5 7.5
What is the left endpoint? 4
(−∞, − 7) ∪ (4, )
![Page 27: 4x 3 9 and 2 5x < 7 - University of Alaska Anchoragemath.uaa.alaska.edu/~afmaf/classes/math105/notes/...Solving Inequalities by Inversion Keywords: equation, solve, solving, inversion](https://reader033.vdocument.in/reader033/viewer/2022050303/5f6bde83ec36804e14223878/html5/thumbnails/27.jpg)
Multiple Inequalities
11− 7x > 60, and 3x− 11 < 1.−7x > 49, and 3x < 12.x < −7, and x > 4.
-10 -7.5 -5 -2.5 0 2.5 5 7.5
What is the right endpoint?
(−∞, − 7) ∪ (4, )
![Page 28: 4x 3 9 and 2 5x < 7 - University of Alaska Anchoragemath.uaa.alaska.edu/~afmaf/classes/math105/notes/...Solving Inequalities by Inversion Keywords: equation, solve, solving, inversion](https://reader033.vdocument.in/reader033/viewer/2022050303/5f6bde83ec36804e14223878/html5/thumbnails/28.jpg)
Multiple Inequalities
11− 7x > 60, and 3x− 11 < 1.−7x > 49, and 3x < 12.x < −7, and x > 4.
-10 -7.5 -5 -2.5 0 2.5 5 7.5
What is the right endpoint? There is none.
(−∞, − 7) ∪ (4,∞)