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Calcmathlete

  • 2 years ago

Find the solution set of the inequality: |2x + 5| + |4x + 7| < 30 How would you do this kind of problem? I'm not familiar with how to do it when there are two separate absolute values...

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  1. sai1234
    • 2 years ago
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    u can write |2x + 5| as2x + 5 or -(2x + 5) like that |4x + 7| as(4x + 7) or -(4x + 7) so totally there as 4 possibilities

  2. Calcmathlete
    • 2 years ago
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    Alright. I'm still a bit confused...would I do them all separately?

  3. experimentX
    • 2 years ago
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    plugin into wolfram ... something interesting there

  4. Calcmathlete
    • 2 years ago
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    lol...it is a bit interesting...I need to know how to do these without wolfram though...

  5. Calcmathlete
    • 2 years ago
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    Is that really what I do?

  6. experimentX
    • 2 years ago
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    i'm not sure .... though this technique seems pretty promising

  7. Calcmathlete
    • 2 years ago
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    But all that results in is the removal of the absolute value no?

  8. experimentX
    • 2 years ago
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    yep ... take square and see |dw:1344019775207:dw|

  9. Calcmathlete
    • 2 years ago
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    I am so confused...not going to lie...if you take the square of both sides, wouldn't you end up with the second side: |dw:1344019964409:dw| and where did the absolute value come back in?

  10. experimentX
    • 2 years ago
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    sorry .. my bad

  11. experimentX
    • 2 years ago
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    |dw:1344020042743:dw|

  12. experimentX
    • 2 years ago
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    looks like this is going to be quite difficult ...

  13. Calcmathlete
    • 2 years ago
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    Yeah...my teacher said that there was a very simple trick to this, but she never had the opportunity to teach it to me, so I'm just stuck on what to do...

  14. experimentX
    • 2 years ago
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    |dw:1344020241753:dw|

  15. experimentX
    • 2 years ago
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    for x is positive.

  16. Calcmathlete
    • 2 years ago
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    Well, turns out that sai at the beginning was correct...you just work out the 4 different cases...

  17. Calcmathlete
    • 2 years ago
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    I found the solution set...

  18. Calcmathlete
    • 2 years ago
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    Thanks for trying though...

  19. experimentX
    • 2 years ago
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    for x is negative, |dw:1344020308613:dw|

  20. experimentX
    • 2 years ago
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    check the value for a = 3, which is less than 30|dw:1344020674321:dw|

  21. experimentX
    • 2 years ago
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    |dw:1344020722686:dw|

  22. experimentX
    • 2 years ago
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    |dw:1344020797357:dw|

  23. Calcmathlete
    • 2 years ago
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    Yup. I get it now. We just test out all 4 possibilities and combine the inequalities. Thank you :)

  24. experimentX
    • 2 years ago
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    well ... the best would be do see carefully how it takes the least effort ...

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