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anonymous

  • one year ago

Graph and solve :)

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  1. anonymous
    • one year ago
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    |dw:1439059109467:dw|

  2. anonymous
    • one year ago
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    @saseal

  3. phi
    • one year ago
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    first step is add +3 to both sides

  4. anonymous
    • one year ago
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    4

  5. phi
    • one year ago
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    you have a "relation" and you must do the same thing to both sides after you add +3 to both sides, what is the new relation?

  6. anonymous
    • one year ago
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    |dw:1439059343639:dw|

  7. phi
    • one year ago
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    yes you could also write it this way \[|x-1| -3 + 3 \le 1+4 \\ |x-1| \le 4 \] the | | mean absolute value. if what is "inside" is positive, you can ignore them for the moment, assume x-1 is 0 or bigger (i.e. positive) then we have \[ x-1 \le 4 \] now what should you add to both sides to get "x by itself" ?

  8. anonymous
    • one year ago
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    x<5

  9. phi
    • one year ago
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    ok now we assume x-1 is negative inside the | | the absolute value signs will make it positive this part is a bit tricky to see (maybe?) but if (x-1) is negative, and we multiply it by -1 we will make it positive in other words *assuming x-1 is negative* then | x-1| is the same thing as -1*(x-1) and we can write \[ -1\cdot (x-1) \le 4 \]

  10. anonymous
    • one year ago
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    so -1x+1<4 ??

  11. phi
    • one year ago
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    yes, now add -1 to both sides

  12. anonymous
    • one year ago
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    but u cant add a -1x to 4 right? Bc they r different terms

  13. anonymous
    • one year ago
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    -1x<3

  14. phi
    • one year ago
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    yes. just add -1 to both sides ok, now you have -x <= 3 (the <= means less than or equal in case you can't type \(\le\))

  15. anonymous
    • one year ago
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    Alright, thanks:) How do ya graph that?

  16. anonymous
    • one year ago
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    Also, wouldnt the sign change since it was divided by a -1??

  17. phi
    • one year ago
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    relations with negative numbers are tricky. *if* we multiply by -1 (on both sides) we have to "flip" the relation however, if we only add or subtract we don't have to worry about that rule we could add +x to both sides -x <= 3 -x + x <= 3 + x 0 <= 3 + x now add -3 to both sides -3+0 <= 3 - 3 + x and finally -3 <= x

  18. phi
    • one year ago
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    -3 <= x means x is equal to or bigger than -3 the other relation (see up above) x<= 5 means x is 5 or smaller both have to be true for the original relation \[ | x -1| - 3 \le 1\] people often write the answer in short form like this\[ -3 \le x \le 5 \]

  19. anonymous
    • one year ago
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    Thanks, how do I graph that on a line?

  20. phi
    • one year ago
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    make a number line with numbers from -3 to 5 put a solid (filled in) circle at -3 and at 5 (this means x could be -3 or -5) and draw a solid line connecting the dots to show x could be any number in between

  21. phi
    • one year ago
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    *could be -3 or +5

  22. anonymous
    • one year ago
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    |dw:1439060288511:dw| like this?

  23. phi
    • one year ago
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    the arrow on the left side is pointing to numbers smaller than -3 (example -4, -5) the answer are \( -3 \le x \) notice the "big" side of the \( \le\) is next to x , which is a clue x is bigger than the other side (the -3) in other words , you want to show that numbers bigger than -3 (such as -2 , -1, 0, etc) are the answer.

  24. anonymous
    • one year ago
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    |dw:1439060533573:dw| That way?

  25. phi
    • one year ago
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    yes, and of course, \( x\le 5\) means x is smaller (notice the small pointy end of the \(\le\) is next to x , which is a clue x is smaller than the "big" side (which has 5)

  26. anonymous
    • one year ago
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    |dw:1439060648200:dw| Like that?

  27. phi
    • one year ago
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    you want your graph to show which numbers make the problem "true" I would leave off the arrow tips because people might interpret that to mean the answer goes forever in that direction. in other words, they would expect just |dw:1439060715000:dw|

  28. anonymous
    • one year ago
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    Ohhh! Thanks so much for all your help:)))

  29. anonymous
    • one year ago
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    im going to post another in the open question section, so if u want to help again...:)

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