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anonymous

  • one year ago

help me solve this equation please? will medal

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  1. anonymous
    • one year ago
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    \[\left| x+1 \right|-3<4\]

  2. anonymous
    • one year ago
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    My answer was x>6

  3. jim_thompson5910
    • one year ago
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    |dw:1441587101373:dw|

  4. anonymous
    • one year ago
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    I'm sorry, it was x<7

  5. jim_thompson5910
    • one year ago
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    This is not an equation. It's an inequality The first step is to add 3 to both sides |dw:1441587163774:dw|

  6. jim_thompson5910
    • one year ago
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    |dw:1441587178859:dw|

  7. jim_thompson5910
    • one year ago
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    so we're left with `|x+1| < 7`

  8. jim_thompson5910
    • one year ago
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    now you'll use the rule If \(\Large |x| < k\) then \(\Large -k < x < k\) where k is a positive number

  9. anonymous
    • one year ago
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    okay

  10. jim_thompson5910
    • one year ago
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    so in this case, that rule makes `|x+1| < 7` turn into `-7 < x+1 < 7`

  11. anonymous
    • one year ago
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    whats our next step?

  12. jim_thompson5910
    • one year ago
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    |dw:1441587371735:dw|

  13. jim_thompson5910
    • one year ago
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    next we subtract 1 from all sides to fully isolate x |dw:1441587398846:dw|

  14. jim_thompson5910
    • one year ago
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    the '1's in the middle cancel since they add to 0 |dw:1441587429310:dw|

  15. anonymous
    • one year ago
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    -6<x<6?

  16. jim_thompson5910
    • one year ago
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    -7 - 1 is not equal to -6

  17. anonymous
    • one year ago
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    on a number line would that look like this?

  18. anonymous
    • one year ago
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    The draw function isnt working for me v.v

  19. anonymous
    • one year ago
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    there would be an open circle at six and the arrow would go to the left continuously?

  20. jim_thompson5910
    • one year ago
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    -7 - 1 = -8 instead think of it as "you're seven dollars in debt. You buy something worth 1 dollar. So you're now 8 dollars in debt"

  21. anonymous
    • one year ago
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    Or would it stop at 8?

  22. jim_thompson5910
    • one year ago
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    `-7 < x+1 < 7` becomes `-8 < x < 6`

  23. jim_thompson5910
    • one year ago
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    |dw:1441587719085:dw|

  24. jim_thompson5910
    • one year ago
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    here's what `-8 < x < 6` looks like |dw:1441587737649:dw| open circle at -8 open circle at 6 shading in between the open circles (do NOT fill in the open circles)

  25. anonymous
    • one year ago
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    Thank you!

  26. jim_thompson5910
    • one year ago
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    you're welcome

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