math 9 lesson #23 – absolute value equations and inequalities mrs. goodman
TRANSCRIPT
![Page 1: Math 9 Lesson #23 – Absolute Value Equations and Inequalities Mrs. Goodman](https://reader036.vdocuments.us/reader036/viewer/2022082713/5697bf7b1a28abf838c8369f/html5/thumbnails/1.jpg)
Math 9Lesson #23 – Absolute Value Equations and
Inequalities
Mrs. Goodman
![Page 2: Math 9 Lesson #23 – Absolute Value Equations and Inequalities Mrs. Goodman](https://reader036.vdocuments.us/reader036/viewer/2022082713/5697bf7b1a28abf838c8369f/html5/thumbnails/2.jpg)
Solving an Absolute Value Equation
|x + 5| = 4
x + 5 = 4 x + 5 = -4
![Page 3: Math 9 Lesson #23 – Absolute Value Equations and Inequalities Mrs. Goodman](https://reader036.vdocuments.us/reader036/viewer/2022082713/5697bf7b1a28abf838c8369f/html5/thumbnails/3.jpg)
Solve each
x + 5 = 4 x + 5 = -4 -5 -5 -5 -5
x = -1 x = -9
![Page 4: Math 9 Lesson #23 – Absolute Value Equations and Inequalities Mrs. Goodman](https://reader036.vdocuments.us/reader036/viewer/2022082713/5697bf7b1a28abf838c8369f/html5/thumbnails/4.jpg)
|3x + 1| + 8 = 10
|3x + 1| = 23x + 1 = 2 3x + 1 = -2
-1 -1 -1 -1
3x = 1 3x = -3 3 3 3 3
x = 1/3 x = -1
![Page 5: Math 9 Lesson #23 – Absolute Value Equations and Inequalities Mrs. Goodman](https://reader036.vdocuments.us/reader036/viewer/2022082713/5697bf7b1a28abf838c8369f/html5/thumbnails/5.jpg)
Solving an Absolute Value Inequality
|x + 5| < 4
x + 5 < 4 x + 5 > -4
![Page 6: Math 9 Lesson #23 – Absolute Value Equations and Inequalities Mrs. Goodman](https://reader036.vdocuments.us/reader036/viewer/2022082713/5697bf7b1a28abf838c8369f/html5/thumbnails/6.jpg)
Solving an Absolute Value Inequality
|x + 3| < 7
x + 3 < 7 x + 3 > -7
![Page 7: Math 9 Lesson #23 – Absolute Value Equations and Inequalities Mrs. Goodman](https://reader036.vdocuments.us/reader036/viewer/2022082713/5697bf7b1a28abf838c8369f/html5/thumbnails/7.jpg)
Solving an Absolute Value Inequality
|x -2| > 8
x - 3 > 8 x - 3 < -8
![Page 8: Math 9 Lesson #23 – Absolute Value Equations and Inequalities Mrs. Goodman](https://reader036.vdocuments.us/reader036/viewer/2022082713/5697bf7b1a28abf838c8369f/html5/thumbnails/8.jpg)
Solving an Absolute Value Inequality
|x + 3| > 8
x + 3 > 8 x + 3 < -8
![Page 9: Math 9 Lesson #23 – Absolute Value Equations and Inequalities Mrs. Goodman](https://reader036.vdocuments.us/reader036/viewer/2022082713/5697bf7b1a28abf838c8369f/html5/thumbnails/9.jpg)
Solving an Absolute Value Inequality
• If you are solving a “less than” or “less than or equal to” absolute value inequality, the graph of your solution will look like an “and” inequality graph.
![Page 10: Math 9 Lesson #23 – Absolute Value Equations and Inequalities Mrs. Goodman](https://reader036.vdocuments.us/reader036/viewer/2022082713/5697bf7b1a28abf838c8369f/html5/thumbnails/10.jpg)
Solving an Absolute Value Inequality
• If you are solving a “greater than” or “greater than or equal to” absolute value inequality, the graph of your solution will look like an “or” inequality graph.
![Page 11: Math 9 Lesson #23 – Absolute Value Equations and Inequalities Mrs. Goodman](https://reader036.vdocuments.us/reader036/viewer/2022082713/5697bf7b1a28abf838c8369f/html5/thumbnails/11.jpg)
Solve
|2x – 5| < 42x – 5 < 4 2x – 5 > -
4 +5 +5 +5 +5 2x < 9 2x > 1 2 2 2 2 x < 9/2 AND x > 1/2
![Page 12: Math 9 Lesson #23 – Absolute Value Equations and Inequalities Mrs. Goodman](https://reader036.vdocuments.us/reader036/viewer/2022082713/5697bf7b1a28abf838c8369f/html5/thumbnails/12.jpg)
Solve
|-2x – 4| > 3-2x – 4 > 3 -2x – 4 < -
3 +4 +4 +4 +4 -2x > 7 -2x < 1 -2 -2 -2 -2 x < -7/2 OR x > -1/2
![Page 13: Math 9 Lesson #23 – Absolute Value Equations and Inequalities Mrs. Goodman](https://reader036.vdocuments.us/reader036/viewer/2022082713/5697bf7b1a28abf838c8369f/html5/thumbnails/13.jpg)
Try these on your own!
1. 3|4x + 1| = 102. |5x| + 1 > 163. |x – 11| < 214. 2|-2x – 7| = 20
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That’s all for the day!
Thanks for working hard!
I’ll see you next time!