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anonymous

  • one year ago

graph/ solve

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  1. anonymous
    • one year ago
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    |dw:1439060839044:dw|

  2. phi
    • one year ago
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    we have negative numbers with a relation so *we have to be careful* the "fast way" is multiply both sides by -1 and *switch the relation operator* the slow (but easy to do) way is add +3 to both sides then add +3 | x-5| to both sides either way, what do you get?

  3. anonymous
    • one year ago
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    0

  4. anonymous
    • one year ago
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    /x-5/<1

  5. phi
    • one year ago
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    do it in steps -3 | x-5| < -3 which way do you want to do it? fast way or slow way?

  6. anonymous
    • one year ago
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    fast way of course!

  7. phi
    • one year ago
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    fast way: multiply both sides by -1 *flip the relation operator*

  8. anonymous
    • one year ago
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    would it be 3/x-5/<3 ??

  9. phi
    • one year ago
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    you did step 1 ok. but step 2 means you change < to > or if you had > you would change it to < or \(\le\) would be changed to \( \ge\) that is the "flip" part

  10. anonymous
    • one year ago
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    3/x-5/>3

  11. phi
    • one year ago
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    yes. the problem with the fast way is you have to remember to flip the operator... if you don't have a good memory for "details", the slow way is safer (one less rule to remember) so now you have 3 | x-5| > 3 it is safe to divide both sides by 3. you get | x-5 | > 1

  12. phi
    • one year ago
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    with absolute value problems we *always* have two conditions either x-5 is positive , in which case , drop the | | or x-5 is negative, in which case we replace the | | with -1*(x-5)

  13. phi
    • one year ago
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    let's do the x-5 is positive condition. we have x-5 > 1 now add +5 to both sides

  14. anonymous
    • one year ago
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    x>6

  15. phi
    • one year ago
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    now do the x-5 is negative case. can you do that one?

  16. anonymous
    • one year ago
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    yes(hopefully)! So i got x<4

  17. phi
    • one year ago
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    looks good. x<4 or x>6 are the solutions put an open circle at 4. the open (not solid , filled in) means 4 is not part of the answer, but we can get as close to 4 as we want (without being exactly 4) and x smaller than 4. all numbers smaller (to the left) of 4 are part of the solution as it would take a long time to draw a line showing all of the numbers, we use an arrow tip to show the answer includes all numbers the arrow points towards.

  18. phi
    • one year ago
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    and then do the same for x> 6 open circle at 6 an arrow pointing which way ??

  19. anonymous
    • one year ago
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    gotcha:) So, the arrows will be pointing in opposite direction x-------->6 and x<----------4 the arrows is showing thee way it'll go:)

  20. phi
    • one year ago
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    yes. one last point: put the answers on the same number line

  21. anonymous
    • one year ago
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    kk. Hold on...|dw:1439061932632:dw|

  22. phi
    • one year ago
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    yes. looks good. for your teacher, make sure the "tick mark" for the 4 is clearly marked (in your graph it is not clear which tick mark is the 4)

  23. anonymous
    • one year ago
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    Will do:)! Thanks again phi<3<3

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