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anonymous

  • 4 years ago

Find the sum of the solutions: 5│x│ - 3 = │3x + 7│

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  1. anonymous
    • 4 years ago
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    \[5\left| x \right|-3 = \left| 3x+7 \right|\]

  2. anonymous
    • 4 years ago
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    How would I go about this?

  3. anonymous
    • 4 years ago
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    Are things in absolute value "like terms?"

  4. anonymous
    • 4 years ago
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    ?

  5. myininaya
    • 4 years ago
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    Let's consider some cases: ------------------------------------------- \[\text{ CASE 1:} x>0 ; x>\frac{-7}{3}\] |x|=x ; |3x+7|=3x+7 5(x)-3=3x+7 solve this for x and then check it -------------------------------------------- \[\text{ CASE 2:} x>0; x<\frac{-7}{3}\] |x|=x; |3x+7|=-(3x+7) 5(x)-3=-(3x+7) solve this for x and check it -------------------------------------------- \[\text{ CASE 3: } x<0; x>\frac{-7}{3}\] |x|=-x ; |3x+7|=3x+7 5(-x)-3=3x+7 solve this for x and check it -------------------------------------------- \[\text{ CASE 4: } x<0 ; x<\frac{-7}{3}\] |x|=-x; |3x+7|=-(3x+7) 5(-x)-3=-(3x+7) solve this for x and check it

  6. anonymous
    • 4 years ago
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    Is that how you have to do it?

  7. anonymous
    • 4 years ago
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    and i dont understand the "Cases"

  8. myininaya
    • 4 years ago
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    i'm looking at when |x|=x or when it is |x|=-x and something for |3x+7|

  9. anonymous
    • 4 years ago
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    what do you mean by something for │3x + 7│

  10. myininaya
    • 4 years ago
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    same thing*

  11. anonymous
    • 4 years ago
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    Can you try to explain it a different way. I'm sorry

  12. myininaya
    • 4 years ago
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    |3x+7|=3x+7 when 3x+7>0 |3x+7|=-(3x+7) when 3x+7<0 |x|=x when x>0 |x|=-x when x<0

  13. myininaya
    • 4 years ago
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    i looked at all possible combinations of these

  14. myininaya
    • 4 years ago
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    that is how i got my 4 cases

  15. anonymous
    • 4 years ago
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    Okay. Thanks. It's more clear now.

  16. myininaya
    • 4 years ago
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    i actually wrote this above when i did the 4 cases

  17. myininaya
    • 4 years ago
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    3x+7>0 => x>-7/3 after solve for x 3x+7<0 => x<-7/3 after solving for x

  18. myininaya
    • 4 years ago
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    i'm glad you understand though :)

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