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OSU - MATH 1075 - Class Notes - Week 3

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OSU - MATH 1075 - Class Notes - Week 3

School: Ohio State University
Department: Math
Course: MATH 1075
Professor: Professor Matthews
Term: Fall 2018
Tags: Math
Name: How draw absolute values
Description: Notes about how to draw absolute values
Uploaded: 08/31/2018
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background image An alternative method to DRAW your way to the solution of an absolute value  inequality  [BUT, be certain you know the ALGEBRAIC approach as well] Where does this approach come from? How far is 3 from 7 on the number line? If we subtract 7 - 3, we find the distance apart, 4 units.   If we subtract 3 - 7, we get - 4, and we want distance to have a positive value. We can put the subtraction work inside an absolute value bracket, and then we don’t have to be  concerned about the order of the subtraction. Like this . . . . |7 - 3| = 4, and |3 - 7| = 4, also. Now, if we see an equation like |x - 2| = 5, and consider what the value of x may be, we can  answer by first thinking, “x and 2 must be EXACTLY 5 units apart” So, let’s draw our way to an answer. Locate 2 on the number line.  Then travel 5 units away, in either direction. If we use - 3 or 7 in the equation, |x - 2| = 5, do they work?  Yep. Solution; x = - 3 or 7 0 - 5 - 2 - 4 - 3 - 1 1 2 3 4 5 7 6 - 6 - 7 - 8 8 4 units apart 0 - 5 - 2 - 4 - 3 - 1 1 2 3 4 5 7 6 - 6 - 7 - 8 8 5 units apart 5 units apart
background image What about |x - 3| ≤ 4? Here we want x to be either EXACTLY 4 units apart from 3, or LESS THAN 4 units away from 3. So we move 4 units away from 3. Solution; [- 1, 7] Let’s try |x - 1| > 6. Here we want x to be MORE THAN 6 units away from 1.  We travel 6 units away from 1. Solution; (-∞, - 5) U (7, ∞) You may have noticed, all examples thus far have been using subtraction, |x - b|.  What do we do when we encounter addition, |x + b|? 0 - 5 - 2 - 4 - 3 - 1 1 2 3 4 5 7 6 - 6 - 7 - 8 8 exactly 4 units 
apart from 3
[ ] All points on the ragged line 
are LESS THAN 4 units away from 3
exactly 4 units 
apart from 3
0 - 5 - 2 - 4 - 3 - 1 1 2 3 4 5 7 6 - 6 - 7 - 8 8 All points on each ragged line 
are MORE THAN 6 units away from 1
( ) exactly 6 units 
apart from 1
exactly 6 units 
apart from 1

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School: Ohio State University
Department: Math
Course: MATH 1075
Professor: Professor Matthews
Term: Fall 2018
Tags: Math
Name: How draw absolute values
Description: Notes about how to draw absolute values
Uploaded: 08/31/2018
5 Pages 25 Views 20 Unlocks
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  • Notes, Study Guides, Flashcards + More!
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