absolute value equations & inequalities eq: how does solving an absolute value...
TRANSCRIPT
![Page 1: Absolute Value Equations & Inequalities EQ: How does solving an absolute value equation/inequality compare to solving a linear equation/inequality?](https://reader035.vdocuments.us/reader035/viewer/2022062314/56649ec55503460f94bcfdef/html5/thumbnails/1.jpg)
Absolute Value Equations & Inequalities
EQ: How does solving an absolute value equation/inequality compare to solving a linear equation/inequality?
![Page 2: Absolute Value Equations & Inequalities EQ: How does solving an absolute value equation/inequality compare to solving a linear equation/inequality?](https://reader035.vdocuments.us/reader035/viewer/2022062314/56649ec55503460f94bcfdef/html5/thumbnails/2.jpg)
I am 3 “miles” from my house
|B| = 3B = 3 or B = -3
![Page 3: Absolute Value Equations & Inequalities EQ: How does solving an absolute value equation/inequality compare to solving a linear equation/inequality?](https://reader035.vdocuments.us/reader035/viewer/2022062314/56649ec55503460f94bcfdef/html5/thumbnails/3.jpg)
Review Absolute Value: the distance a number
is from zero (always positive)
Ex 1) |7| =
Ex 2) |-5| =
Ex 3) 5|2 – 4| + 2 =
![Page 4: Absolute Value Equations & Inequalities EQ: How does solving an absolute value equation/inequality compare to solving a linear equation/inequality?](https://reader035.vdocuments.us/reader035/viewer/2022062314/56649ec55503460f94bcfdef/html5/thumbnails/4.jpg)
Ex 1) Solve: |x| = 8
Ex 2) Solve: |x| = 25
Ex 3) Solve: |x| = -10
Absolute Value Equations
![Page 5: Absolute Value Equations & Inequalities EQ: How does solving an absolute value equation/inequality compare to solving a linear equation/inequality?](https://reader035.vdocuments.us/reader035/viewer/2022062314/56649ec55503460f94bcfdef/html5/thumbnails/5.jpg)
Have two solutions because the absolute
value of a positive number is the same
as the absolute value of a negative
number.
![Page 6: Absolute Value Equations & Inequalities EQ: How does solving an absolute value equation/inequality compare to solving a linear equation/inequality?](https://reader035.vdocuments.us/reader035/viewer/2022062314/56649ec55503460f94bcfdef/html5/thumbnails/6.jpg)
Solving Absolute Value Equations
Step 1: Get “bars” alone on one side
Step 2: Re-write as two equations; flip the
signs on the RIGHT side (drop the bars)
Step 3: Solve both equations
Step 4: Check for an extraneous solution!!
![Page 7: Absolute Value Equations & Inequalities EQ: How does solving an absolute value equation/inequality compare to solving a linear equation/inequality?](https://reader035.vdocuments.us/reader035/viewer/2022062314/56649ec55503460f94bcfdef/html5/thumbnails/7.jpg)
Extraneous Solution A value you get after correctly solving
the problem that does not actually satisfy the equation.
![Page 8: Absolute Value Equations & Inequalities EQ: How does solving an absolute value equation/inequality compare to solving a linear equation/inequality?](https://reader035.vdocuments.us/reader035/viewer/2022062314/56649ec55503460f94bcfdef/html5/thumbnails/8.jpg)
Ex 4)
3|x + 2| - 7 = 14
3|x + 2| = 21
|x + 2| = 7
![Page 9: Absolute Value Equations & Inequalities EQ: How does solving an absolute value equation/inequality compare to solving a linear equation/inequality?](https://reader035.vdocuments.us/reader035/viewer/2022062314/56649ec55503460f94bcfdef/html5/thumbnails/9.jpg)
|x + 2| = 7
x + 2 = 7 x + 2 = -7 x = 5 or x = -9
![Page 10: Absolute Value Equations & Inequalities EQ: How does solving an absolute value equation/inequality compare to solving a linear equation/inequality?](https://reader035.vdocuments.us/reader035/viewer/2022062314/56649ec55503460f94bcfdef/html5/thumbnails/10.jpg)
Check Your Answers:
x = 5 x = -9
3|x + 2| - 7 = 14 3|x + 2| - 7 = 14
3|5 + 2| - 7 = 14 3|-9 + 2| - 7 = 14
3|7| - 7 = 14 3|-7| - 7 = 14
14 = 14 14 = 14
![Page 11: Absolute Value Equations & Inequalities EQ: How does solving an absolute value equation/inequality compare to solving a linear equation/inequality?](https://reader035.vdocuments.us/reader035/viewer/2022062314/56649ec55503460f94bcfdef/html5/thumbnails/11.jpg)
Ex 5)
|3x + 2| = 4x + 5
3x + 2 = 4x + 5
3x + 2 = -4x – 5
![Page 12: Absolute Value Equations & Inequalities EQ: How does solving an absolute value equation/inequality compare to solving a linear equation/inequality?](https://reader035.vdocuments.us/reader035/viewer/2022062314/56649ec55503460f94bcfdef/html5/thumbnails/12.jpg)
3x + 2 = 4x + 5
3x + 2 = -4x – 5
![Page 13: Absolute Value Equations & Inequalities EQ: How does solving an absolute value equation/inequality compare to solving a linear equation/inequality?](https://reader035.vdocuments.us/reader035/viewer/2022062314/56649ec55503460f94bcfdef/html5/thumbnails/13.jpg)
|3x + 2| = 4x + 5
Check Your Solutions
![Page 14: Absolute Value Equations & Inequalities EQ: How does solving an absolute value equation/inequality compare to solving a linear equation/inequality?](https://reader035.vdocuments.us/reader035/viewer/2022062314/56649ec55503460f94bcfdef/html5/thumbnails/14.jpg)
Ex 6)
|x – 4| + 7 = 2
|x – 4| = -5
NO SOLUTION
![Page 15: Absolute Value Equations & Inequalities EQ: How does solving an absolute value equation/inequality compare to solving a linear equation/inequality?](https://reader035.vdocuments.us/reader035/viewer/2022062314/56649ec55503460f94bcfdef/html5/thumbnails/15.jpg)
Solving by Graphing
Step 1: Enter the left & right side into Y1 & Y2
PRESS → NUM #1 abs(
Step 2: Find the first intersection
Step 3: Find the second intersection if there is one
MATH
2nd TRACE #5
![Page 16: Absolute Value Equations & Inequalities EQ: How does solving an absolute value equation/inequality compare to solving a linear equation/inequality?](https://reader035.vdocuments.us/reader035/viewer/2022062314/56649ec55503460f94bcfdef/html5/thumbnails/16.jpg)
3|x + 2| -7 = 14
![Page 17: Absolute Value Equations & Inequalities EQ: How does solving an absolute value equation/inequality compare to solving a linear equation/inequality?](https://reader035.vdocuments.us/reader035/viewer/2022062314/56649ec55503460f94bcfdef/html5/thumbnails/17.jpg)
|3x + 2| = 4x + 5
![Page 18: Absolute Value Equations & Inequalities EQ: How does solving an absolute value equation/inequality compare to solving a linear equation/inequality?](https://reader035.vdocuments.us/reader035/viewer/2022062314/56649ec55503460f94bcfdef/html5/thumbnails/18.jpg)
Practice
1) Solve: |5x| + 10 = 55
2) Solve: |x – 3| = 10
3) Solve: 2|y + 6| = 8
4) Solve: |a – 5| + 3 = 2
5) Solve: |4x + 9| = 5x + 18
![Page 19: Absolute Value Equations & Inequalities EQ: How does solving an absolute value equation/inequality compare to solving a linear equation/inequality?](https://reader035.vdocuments.us/reader035/viewer/2022062314/56649ec55503460f94bcfdef/html5/thumbnails/19.jpg)
Thank about it… If |x| < 5 what are some possible values
of x?
If |x| > 5 what are some possible values of x?
![Page 20: Absolute Value Equations & Inequalities EQ: How does solving an absolute value equation/inequality compare to solving a linear equation/inequality?](https://reader035.vdocuments.us/reader035/viewer/2022062314/56649ec55503460f94bcfdef/html5/thumbnails/20.jpg)
Solving Absolute Value Inequalities
Since the inequalities are absolute value, there are still going to be two solutions
When writing the second equation, be sure to flip the inequality sign.
Also, when dividing by a negative the inequality sign flips.
![Page 21: Absolute Value Equations & Inequalities EQ: How does solving an absolute value equation/inequality compare to solving a linear equation/inequality?](https://reader035.vdocuments.us/reader035/viewer/2022062314/56649ec55503460f94bcfdef/html5/thumbnails/21.jpg)
Ex 1)
![Page 22: Absolute Value Equations & Inequalities EQ: How does solving an absolute value equation/inequality compare to solving a linear equation/inequality?](https://reader035.vdocuments.us/reader035/viewer/2022062314/56649ec55503460f94bcfdef/html5/thumbnails/22.jpg)
Ex 2)
![Page 23: Absolute Value Equations & Inequalities EQ: How does solving an absolute value equation/inequality compare to solving a linear equation/inequality?](https://reader035.vdocuments.us/reader035/viewer/2022062314/56649ec55503460f94bcfdef/html5/thumbnails/23.jpg)
You Try! Solve | 2x + 3 | < 6
![Page 24: Absolute Value Equations & Inequalities EQ: How does solving an absolute value equation/inequality compare to solving a linear equation/inequality?](https://reader035.vdocuments.us/reader035/viewer/2022062314/56649ec55503460f94bcfdef/html5/thumbnails/24.jpg)
Ex 3) Solve 423 xx
![Page 25: Absolute Value Equations & Inequalities EQ: How does solving an absolute value equation/inequality compare to solving a linear equation/inequality?](https://reader035.vdocuments.us/reader035/viewer/2022062314/56649ec55503460f94bcfdef/html5/thumbnails/25.jpg)
You Try! Solve |2x-5|>x+1.
![Page 26: Absolute Value Equations & Inequalities EQ: How does solving an absolute value equation/inequality compare to solving a linear equation/inequality?](https://reader035.vdocuments.us/reader035/viewer/2022062314/56649ec55503460f94bcfdef/html5/thumbnails/26.jpg)
Quick Write: Think of some objects or situations that need
to be within a certain “value” – if you go too much over it would be a bad thing, and if you go too much under it would also be a bad thing:
![Page 27: Absolute Value Equations & Inequalities EQ: How does solving an absolute value equation/inequality compare to solving a linear equation/inequality?](https://reader035.vdocuments.us/reader035/viewer/2022062314/56649ec55503460f94bcfdef/html5/thumbnails/27.jpg)
Tolerance
There are strict height requirements to be a “Rockette”
You must be between 66 inches 70.5 inches
![Page 28: Absolute Value Equations & Inequalities EQ: How does solving an absolute value equation/inequality compare to solving a linear equation/inequality?](https://reader035.vdocuments.us/reader035/viewer/2022062314/56649ec55503460f94bcfdef/html5/thumbnails/28.jpg)
Perfect Amount
LeastAllowed
MostAllowed
Tolerance Tolerance
Tolerance: The difference between a desired
measurement and its maximum and minimum allowable values.
![Page 29: Absolute Value Equations & Inequalities EQ: How does solving an absolute value equation/inequality compare to solving a linear equation/inequality?](https://reader035.vdocuments.us/reader035/viewer/2022062314/56649ec55503460f94bcfdef/html5/thumbnails/29.jpg)
Ex 1) The doctor says that you need to stay between 125 and 135 lbs to be at a healthy weight.
Min: _______ Perfect: _______ Max: ________
Tolerance: __________
![Page 30: Absolute Value Equations & Inequalities EQ: How does solving an absolute value equation/inequality compare to solving a linear equation/inequality?](https://reader035.vdocuments.us/reader035/viewer/2022062314/56649ec55503460f94bcfdef/html5/thumbnails/30.jpg)
Example 2) Workers at a hardware store take their
morning break no earlier than 10 am and no later than noon. Let c represent the time the workers take their break. Write an absolute value inequality to represent the situation.
![Page 31: Absolute Value Equations & Inequalities EQ: How does solving an absolute value equation/inequality compare to solving a linear equation/inequality?](https://reader035.vdocuments.us/reader035/viewer/2022062314/56649ec55503460f94bcfdef/html5/thumbnails/31.jpg)
![Page 32: Absolute Value Equations & Inequalities EQ: How does solving an absolute value equation/inequality compare to solving a linear equation/inequality?](https://reader035.vdocuments.us/reader035/viewer/2022062314/56649ec55503460f94bcfdef/html5/thumbnails/32.jpg)
![Page 33: Absolute Value Equations & Inequalities EQ: How does solving an absolute value equation/inequality compare to solving a linear equation/inequality?](https://reader035.vdocuments.us/reader035/viewer/2022062314/56649ec55503460f94bcfdef/html5/thumbnails/33.jpg)
![Page 34: Absolute Value Equations & Inequalities EQ: How does solving an absolute value equation/inequality compare to solving a linear equation/inequality?](https://reader035.vdocuments.us/reader035/viewer/2022062314/56649ec55503460f94bcfdef/html5/thumbnails/34.jpg)
![Page 35: Absolute Value Equations & Inequalities EQ: How does solving an absolute value equation/inequality compare to solving a linear equation/inequality?](https://reader035.vdocuments.us/reader035/viewer/2022062314/56649ec55503460f94bcfdef/html5/thumbnails/35.jpg)
![Page 36: Absolute Value Equations & Inequalities EQ: How does solving an absolute value equation/inequality compare to solving a linear equation/inequality?](https://reader035.vdocuments.us/reader035/viewer/2022062314/56649ec55503460f94bcfdef/html5/thumbnails/36.jpg)
![Page 37: Absolute Value Equations & Inequalities EQ: How does solving an absolute value equation/inequality compare to solving a linear equation/inequality?](https://reader035.vdocuments.us/reader035/viewer/2022062314/56649ec55503460f94bcfdef/html5/thumbnails/37.jpg)
![Page 38: Absolute Value Equations & Inequalities EQ: How does solving an absolute value equation/inequality compare to solving a linear equation/inequality?](https://reader035.vdocuments.us/reader035/viewer/2022062314/56649ec55503460f94bcfdef/html5/thumbnails/38.jpg)
![Page 39: Absolute Value Equations & Inequalities EQ: How does solving an absolute value equation/inequality compare to solving a linear equation/inequality?](https://reader035.vdocuments.us/reader035/viewer/2022062314/56649ec55503460f94bcfdef/html5/thumbnails/39.jpg)
Exit Ticket: How is solving an absolute value inequality
different than solving an absolute value equation?
What is the difference between the solutions of an equation and the solutions of an inequality?