Geometric Interpretation of Absolute Value: If a and b are points on a number line, then |a – b| may be interpreted geometrically as the distance between the points a and b on a number line. In other words: |a-b|=the distance between a and b on a number line Examples: Algebraic Statement Geometric Interpretation |5–3|=2 On a number line, the distance between 5 and 3 is 2 |B – 4|>7 On a number line, the distance between B and 4 is more than 7 1. Express the given geometric statement about numbers on the number line algebraically, using absolute values. a) The distance between 5 and P is at most 4. b) x is more than T units from 5. c) The distance between A and -2 is less than 7. d) x is closer to -3 than to 8. 2. For each of the following algebraic expressions, give a geometric interpretation. a) |x-4|=3 b) |x+2|>7 2.1.pdf
Geometric Interpretation of Absolute Value: If a and b are points on a number line, then |a – b| may be interpreted geometrically as the distance between the points a and b on a number line. In other words: |a-b|=the distance between a and b on a number line Examples: Algebraic Statement Geometric Interpretation |5–3|=2 On a number line, the distance between 5 and 3 is 2 |B – 4|>7 On a number line, the distance between B and 4 is more than 7 1. Express the given geometric statement about numbers on the number line algebraically, using absolute values. a) The distance between 5 and P is at most 4. b) x is more than T units from 5. c) The distance between A and -2 is less than 7. d) x is closer to -3 than to 8. 2. For each of the following algebraic expressions, give a geometric interpretation. a) |x-4|=3 b) |x+2|>7 2.1.pdf
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.1: Real Numbers
Problem 23E
Related questions
Question
![Geometric Interpretation of Absolute Value:
If a and b are points on a number line, then |a -b| may be interpreted geometrically as the distance
between the points a and b on a number line. In other words:
|a -b|= the distance between a and b on a number line
Еxamples:
Algebraic Statement
Geometric Interpretation
|5–3|=2
On a number line, the distance between 5 and 3 is 2
|B – 4|>7
On a number line, the distance between B and 4 is more than 7
1. Express the given geometric statement about numbers on the number line algebraically, using absolute
values.
a) The distance between 5 and P is at most 4.
b) x is more than T units from 5.
c) The distance between A and -2 is less than 7.
d) x is closer to -3 than to 8.
2. For each of the following algebraic expressions, give a geometric interpretation.
a) |x- 4|=3
b) |x+2|>7
nl
2.1.pdf](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F04ddd72f-30f0-437a-bf8b-c24526128137%2Fe47739de-bb5d-4ba5-abbf-a49b86642a96%2F1wtpbk_processed.png&w=3840&q=75)
Transcribed Image Text:Geometric Interpretation of Absolute Value:
If a and b are points on a number line, then |a -b| may be interpreted geometrically as the distance
between the points a and b on a number line. In other words:
|a -b|= the distance between a and b on a number line
Еxamples:
Algebraic Statement
Geometric Interpretation
|5–3|=2
On a number line, the distance between 5 and 3 is 2
|B – 4|>7
On a number line, the distance between B and 4 is more than 7
1. Express the given geometric statement about numbers on the number line algebraically, using absolute
values.
a) The distance between 5 and P is at most 4.
b) x is more than T units from 5.
c) The distance between A and -2 is less than 7.
d) x is closer to -3 than to 8.
2. For each of the following algebraic expressions, give a geometric interpretation.
a) |x- 4|=3
b) |x+2|>7
nl
2.1.pdf
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