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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
    • one year ago
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    Example:

  2. anonymous
    • one year ago
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    I thought distance was always supposed to be negative, but some of the answers to my questions use a positive.

  3. LynFran
    • one year ago
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    no distance is always positive

  4. anonymous
    • one year ago
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    The answers use negatives.

  5. LynFran
    • one year ago
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    because we are talking about absolute values .... we usually get 2 answers one is positive and one is negative..

  6. LynFran
    • one year ago
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    @DecentNabeel wat do u think..?

  7. triciaal
    • one year ago
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    distance is always a positive unit of measure between 2 points

  8. LynFran
    • one year ago
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    for absolute .... example |x+3|=5 then (x+3)=+5 and (x+3)=-5

  9. triciaal
    • one year ago
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    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
    • one year ago
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    I'm not solving an actual absolute value inequality, I am trying to write absolute value inequalities using a graph.

  11. triciaal
    • one year ago
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    read again slowly

  12. triciaal
    • one year ago
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    solve each and put the results on the same graph to see the final solution

  13. anonymous
    • one year ago
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    There is nothing to solve. I already have the graphs, and am working backwards to find the inequality.

  14. triciaal
    • one year ago
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    look at number 25

  15. triciaal
    • one year ago
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    x > -12 and x< -6

  16. freckles
    • one year ago
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    \[\text{ assume } a \text{ is positive } \\ |x-c| \le a \text{ means we are shading the interval }[ c-a , c+a] \\ |x-c| \ge a \text{ means we are shading everything outside the interval } (c-a,c+a)\]

  17. triciaal
    • one year ago
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    |dw:1440897882997:dw|

  18. triciaal
    • one year ago
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    |dw:1440898166918:dw|

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

  21. freckles
    • one year ago
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    notice in the first graph you put c=-9 and a=3 the second one you have c=1 and a=2

  22. freckles
    • one year ago
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    i think a couple of my a's above looks like 2's but they are a's

  23. freckles
    • one year ago
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    |dw:1440898758376:dw|

  24. freckles
    • one year ago
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    |dw:1440898823346:dw| can you guess how to represent this

  25. anonymous
    • one year ago
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    |x-2|<-5

  26. freckles
    • one year ago
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    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
    • one year ago
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    |dw:1440899046041:dw|

  28. anonymous
    • one year ago
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    \[|x-3.5|\le4.5\]

  29. freckles
    • one year ago
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    let's try another one |dw:1440899271018:dw|*

  30. freckles
    • one year ago
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    you are awesome

  31. freckles
    • one year ago
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    I made a type-o and you still figured out

  32. freckles
    • one year ago
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    |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
    • one year ago
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    |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
    • one year ago
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    anyways do you have any questions?

  35. anonymous
    • one year ago
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    But how do you know when to write the inequality as a negative or a positive?

  36. freckles
    • one year ago
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    what do you mean

  37. anonymous
    • one year ago
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    Like, you had |x-5|>1 and |x+5|<2 How do you know when to put negative and positive

  38. freckles
    • one year ago
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    we only had |x-5|>1 for previous one

  39. anonymous
    • one year ago
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    Yes, but how did you know to put a negative.

  40. freckles
    • one year ago
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    |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
    • one year ago
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    |x-5|>1 means x-5<-1 or x-5>1 which means x<4 or x>6 |dw:1440899857523:dw|

  42. freckles
    • one year ago
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    |x-5|>1 looks like this: |dw:1440899886515:dw| while |x-(-5)|>1 looks like this: |dw:1440899916458:dw|

  43. freckles
    • one year ago
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    by the way |x-(-5)|>1 is the same as saying |x+5|>1 since -(-5)=+5

  44. freckles
    • one year ago
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    |x-c|<=a says we want all numbers a units away from c in both directions

  45. freckles
    • one year ago
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    and yes c can be a positive or negative number

  46. anonymous
    • one year ago
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    Ohhhhh! I finally understand!

  47. anonymous
    • one year ago
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    Thanks for your help!

  48. freckles
    • one year ago
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    np

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