## anonymous one year ago How do you determine when to use addition or subtraction when solving an absolute value inequality using a graph?

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1. anonymous

Example:

2. anonymous

I thought distance was always supposed to be negative, but some of the answers to my questions use a positive.

3. LynFran

no distance is always positive

4. anonymous

5. LynFran

because we are talking about absolute values .... we usually get 2 answers one is positive and one is negative..

6. LynFran

@DecentNabeel wat do u think..?

7. triciaal

distance is always a positive unit of measure between 2 points

8. LynFran

for absolute .... example |x+3|=5 then (x+3)=+5 and (x+3)=-5

9. triciaal

one approach to doing absolute value problems is to split in 2 the positive and the negative solve each then find the combined solution

10. anonymous

I'm not solving an actual absolute value inequality, I am trying to write absolute value inequalities using a graph.

11. triciaal

12. triciaal

solve each and put the results on the same graph to see the final solution

13. anonymous

There is nothing to solve. I already have the graphs, and am working backwards to find the inequality.

14. triciaal

look at number 25

15. triciaal

x > -12 and x< -6

16. freckles

$\text{ assume } a \text{ is positive } \\ |x-c| \le a \text{ means we are shading the interval }[ c-a , c+a] \\ |x-c| \ge a \text{ means we are shading everything outside the interval } (c-a,c+a)$

17. triciaal

|dw:1440897882997:dw|

18. triciaal

|dw:1440898166918:dw|

19. anonymous

I don't need to solve it. The answer was |x+9|<3 I need to know when to use addition or subtraction when solving from a graph.

20. freckles

$\text{ assume } a \text{ is positive } \\ |x-c| \le a \text{ means we are shading the interval }[ c-a , c+a] \\ |x-c| \ge a \text{ means we are shading everything outside the interval } (c-a,c+a)$ |dw:1440898355091:dw| |dw:1440898407502:dw| I have added drawings in case you didn't understood my words

21. freckles

notice in the first graph you put c=-9 and a=3 the second one you have c=1 and a=2

22. freckles

i think a couple of my a's above looks like 2's but they are a's

23. freckles

|dw:1440898758376:dw|

24. freckles

|dw:1440898823346:dw| can you guess how to represent this

25. anonymous

|x-2|<-5

26. freckles

we have open circles so we don't want an equality thing in there at all we also want a < symbol since our shading is between the numbers now the first thing to notice is the center number which is -5 that is our c and a is how far the exterior numbers are away which is 2 |x-(-5)|<2 |x+5|<2

27. freckles

|dw:1440899046041:dw|

28. anonymous

$|x-3.5|\le4.5$

29. freckles

let's try another one |dw:1440899271018:dw|*

30. freckles

you are awesome

31. freckles

I made a type-o and you still figured out

32. freckles

|dw:1440899357439:dw| yes the center number is 3.5 so you c is 3.5 and 3.5 is 4.5 units from 8 and 3.5 is 4.5 units from -1 so we have $|x-3.5| \le 4.5$

33. freckles

|dw:1440899526070:dw| the center number here is 5 and your a is 1 since both 4 and 6 are 1 unit from 5 $|x-5| >1$

34. freckles

anyways do you have any questions?

35. anonymous

But how do you know when to write the inequality as a negative or a positive?

36. freckles

what do you mean

37. anonymous

Like, you had |x-5|>1 and |x+5|<2 How do you know when to put negative and positive

38. freckles

we only had |x-5|>1 for previous one

39. anonymous

Yes, but how did you know to put a negative.

40. freckles

|x-(-5)|>1 would be right if -5 was at the center and to the right you had -5+1 and to the left you had -5-1 instead

41. freckles

|x-5|>1 means x-5<-1 or x-5>1 which means x<4 or x>6 |dw:1440899857523:dw|

42. freckles

|x-5|>1 looks like this: |dw:1440899886515:dw| while |x-(-5)|>1 looks like this: |dw:1440899916458:dw|

43. freckles

by the way |x-(-5)|>1 is the same as saying |x+5|>1 since -(-5)=+5

44. freckles

|x-c|<=a says we want all numbers a units away from c in both directions

45. freckles

and yes c can be a positive or negative number

46. anonymous

Ohhhhh! I finally understand!

47. anonymous