Math Pacing Solving Open Sentences Involving Absolute Value – 3– 2– 10123456...
-
Upload
constance-greene -
Category
Documents
-
view
221 -
download
0
Transcript of Math Pacing Solving Open Sentences Involving Absolute Value – 3– 2– 10123456...
![Page 1: Math Pacing Solving Open Sentences Involving Absolute Value – 3– 2– 10123456 |||||||||||||||||||| – 5– 4– 3– 2– 101234 ||||||||||||||||||||](https://reader035.fdocuments.in/reader035/viewer/2022081511/56649f3e5503460f94c5f098/html5/thumbnails/1.jpg)
Solving Open Sentences Involving Absolute Value
5or2| xxx– 3 – 2 – 1 0 1 2 3 4 5 6| | | | | | | | | |
34| xx– 5 – 4 – 3 – 2 – 1 0 1 2 3 4| | | | | | | | | |
5or2| xxx
![Page 2: Math Pacing Solving Open Sentences Involving Absolute Value – 3– 2– 10123456 |||||||||||||||||||| – 5– 4– 3– 2– 101234 ||||||||||||||||||||](https://reader035.fdocuments.in/reader035/viewer/2022081511/56649f3e5503460f94c5f098/html5/thumbnails/2.jpg)
Solving Open Sentences Involving Absolute ValueThere are three types of open sentences that can involve absolute value.
nx nx nx Consider the case | x | = n.
| x | = 5 means the distance between 0 and x is 5 units
If | x | = 5, then x = – 5 or x = 5.
The solution set is {– 5, 5}.
![Page 3: Math Pacing Solving Open Sentences Involving Absolute Value – 3– 2– 10123456 |||||||||||||||||||| – 5– 4– 3– 2– 101234 ||||||||||||||||||||](https://reader035.fdocuments.in/reader035/viewer/2022081511/56649f3e5503460f94c5f098/html5/thumbnails/3.jpg)
Solving Open Sentences Involving Absolute Value
Case 1 The value inside the absolute value symbols is positive.
Case 2 The value inside the absolute value symbols is negative.
When solving equations that involve absolute value, there are two cases to consider:
Equations involving absolute value can be solved by graphing them on a number line or by writing them as a compound sentence and solving it.
![Page 4: Math Pacing Solving Open Sentences Involving Absolute Value – 3– 2– 10123456 |||||||||||||||||||| – 5– 4– 3– 2– 101234 ||||||||||||||||||||](https://reader035.fdocuments.in/reader035/viewer/2022081511/56649f3e5503460f94c5f098/html5/thumbnails/4.jpg)
Method 1 Graphing
means that the distance between b and –6 is 5 units. To find b on the number line, start at –6 and move 5 units in either direction.
The distance from –6 to –11 is 5 units.
The distance from –6 to –1 is 5 units.
Answer: The solution set is
Solve an Absolute Value Equation
![Page 5: Math Pacing Solving Open Sentences Involving Absolute Value – 3– 2– 10123456 |||||||||||||||||||| – 5– 4– 3– 2– 101234 ||||||||||||||||||||](https://reader035.fdocuments.in/reader035/viewer/2022081511/56649f3e5503460f94c5f098/html5/thumbnails/5.jpg)
Method 2 Compound Sentence
Answer: The solution set is
Write as or
Original inequality
Subtract 6 from each side.
Case 1 Case 2
Simplify.
Solve an Absolute Value Equation
![Page 6: Math Pacing Solving Open Sentences Involving Absolute Value – 3– 2– 10123456 |||||||||||||||||||| – 5– 4– 3– 2– 101234 ||||||||||||||||||||](https://reader035.fdocuments.in/reader035/viewer/2022081511/56649f3e5503460f94c5f098/html5/thumbnails/6.jpg)
Answer: {12, –2}
Solve an Absolute Value Equation
![Page 7: Math Pacing Solving Open Sentences Involving Absolute Value – 3– 2– 10123456 |||||||||||||||||||| – 5– 4– 3– 2– 101234 ||||||||||||||||||||](https://reader035.fdocuments.in/reader035/viewer/2022081511/56649f3e5503460f94c5f098/html5/thumbnails/7.jpg)
Write an equation involving the absolute value for the graph.
Find the point that is the same distance from –4 as the distance from 6. The midpoint between –4 and 6 is 1.
The distance from 1 to –4 is 5 units.
The distance from 1 to 6 is 5 units.So, an equation is .
Write an Absolute Value Equation
![Page 8: Math Pacing Solving Open Sentences Involving Absolute Value – 3– 2– 10123456 |||||||||||||||||||| – 5– 4– 3– 2– 101234 ||||||||||||||||||||](https://reader035.fdocuments.in/reader035/viewer/2022081511/56649f3e5503460f94c5f098/html5/thumbnails/8.jpg)
Check Substitute –4 and 6 into
Answer:
Write an Absolute Value Equation
![Page 9: Math Pacing Solving Open Sentences Involving Absolute Value – 3– 2– 10123456 |||||||||||||||||||| – 5– 4– 3– 2– 101234 ||||||||||||||||||||](https://reader035.fdocuments.in/reader035/viewer/2022081511/56649f3e5503460f94c5f098/html5/thumbnails/9.jpg)
Write an equation involving the absolute value for the graph.
Answer:
Write an Absolute Value Equation
![Page 10: Math Pacing Solving Open Sentences Involving Absolute Value – 3– 2– 10123456 |||||||||||||||||||| – 5– 4– 3– 2– 101234 ||||||||||||||||||||](https://reader035.fdocuments.in/reader035/viewer/2022081511/56649f3e5503460f94c5f098/html5/thumbnails/10.jpg)
Solving Open Sentences Involving Absolute Value
Consider the case | x | < n.
| x | < 5 means the distance between 0 and x is LESS than 5 units
If | x | < 5, then x > – 5 and x < 5.
The solution set is {x| – 5 < x < 5}.
![Page 11: Math Pacing Solving Open Sentences Involving Absolute Value – 3– 2– 10123456 |||||||||||||||||||| – 5– 4– 3– 2– 101234 ||||||||||||||||||||](https://reader035.fdocuments.in/reader035/viewer/2022081511/56649f3e5503460f94c5f098/html5/thumbnails/11.jpg)
Solving Open Sentences Involving Absolute Value
Case 1 The value inside the absolute value symbols is less than the positive value of n.
Case 2 The value inside the absolute value symbols is greater than negative value of n.
When solving equations of the form | x | < n, find the intersection of these two cases.
![Page 12: Math Pacing Solving Open Sentences Involving Absolute Value – 3– 2– 10123456 |||||||||||||||||||| – 5– 4– 3– 2– 101234 ||||||||||||||||||||](https://reader035.fdocuments.in/reader035/viewer/2022081511/56649f3e5503460f94c5f098/html5/thumbnails/12.jpg)
Then graph the solution set.
Write as and
Original inequality
Add 3 to each side.
Simplify.
Case 1 Case 2
Answer: The solution set is
Solve an Absolute Value Inequality (<)
![Page 13: Math Pacing Solving Open Sentences Involving Absolute Value – 3– 2– 10123456 |||||||||||||||||||| – 5– 4– 3– 2– 101234 ||||||||||||||||||||](https://reader035.fdocuments.in/reader035/viewer/2022081511/56649f3e5503460f94c5f098/html5/thumbnails/13.jpg)
Then graph the solution set.
Answer:
Solve an Absolute Value Inequality (<)
![Page 14: Math Pacing Solving Open Sentences Involving Absolute Value – 3– 2– 10123456 |||||||||||||||||||| – 5– 4– 3– 2– 101234 ||||||||||||||||||||](https://reader035.fdocuments.in/reader035/viewer/2022081511/56649f3e5503460f94c5f098/html5/thumbnails/14.jpg)
Solving Open Sentences Involving Absolute Value
Consider the case | x | > n.
| x | > 5 means the distance between 0 and x is GREATER than 5 units
If | x | > 5, then x < – 5 or x > 5.
The solution set is {x| x < – 5 or x > 5}.
![Page 15: Math Pacing Solving Open Sentences Involving Absolute Value – 3– 2– 10123456 |||||||||||||||||||| – 5– 4– 3– 2– 101234 ||||||||||||||||||||](https://reader035.fdocuments.in/reader035/viewer/2022081511/56649f3e5503460f94c5f098/html5/thumbnails/15.jpg)
Solving Open Sentences Involving Absolute Value
Case 1 The value inside the absolute value symbols is greater than the positive value of n.
Case 2 The value inside the absolute value symbols is less than negative value of n.
When solving equations of the form | x | > n, find the union of these two cases.
![Page 16: Math Pacing Solving Open Sentences Involving Absolute Value – 3– 2– 10123456 |||||||||||||||||||| – 5– 4– 3– 2– 101234 ||||||||||||||||||||](https://reader035.fdocuments.in/reader035/viewer/2022081511/56649f3e5503460f94c5f098/html5/thumbnails/16.jpg)
Case 1 Case 2
Then graph the solution set.
Write as or
Add 3 to each side.
Simplify.
Original inequality
Divide each side by 3.
Simplify.
Solve an Absolute Value Inequality (>)
![Page 17: Math Pacing Solving Open Sentences Involving Absolute Value – 3– 2– 10123456 |||||||||||||||||||| – 5– 4– 3– 2– 101234 ||||||||||||||||||||](https://reader035.fdocuments.in/reader035/viewer/2022081511/56649f3e5503460f94c5f098/html5/thumbnails/17.jpg)
Answer: The solution set is
Solve an Absolute Value Inequality (>)
![Page 18: Math Pacing Solving Open Sentences Involving Absolute Value – 3– 2– 10123456 |||||||||||||||||||| – 5– 4– 3– 2– 101234 ||||||||||||||||||||](https://reader035.fdocuments.in/reader035/viewer/2022081511/56649f3e5503460f94c5f098/html5/thumbnails/18.jpg)
Then graph the solution set.
Answer:
Solve an Absolute Value Inequality (>)
![Page 19: Math Pacing Solving Open Sentences Involving Absolute Value – 3– 2– 10123456 |||||||||||||||||||| – 5– 4– 3– 2– 101234 ||||||||||||||||||||](https://reader035.fdocuments.in/reader035/viewer/2022081511/56649f3e5503460f94c5f098/html5/thumbnails/19.jpg)
Solving Open Sentences Involving Absolute Value
In general, there are three rules to remember when solving equations and inequalities involving absolute value:
1. If then or (solution set of two numbers)
2. If then and
(intersection of inequalities)
3. If then or(union of inequalities)
nx
nx
nx
nx nx
nx nx
nx nx
nxn