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anonymous

  • 5 years ago

solve: |x=6|-4=2

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  1. anonymous
    • 5 years ago
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    |x+6|-4=2

  2. myininaya
    • 5 years ago
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    abs(x+6)=2+4=6 abs(x+6)=6 x+6=6 and x+6=-6 x=0 x=-12

  3. myininaya
    • 5 years ago
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    example: abs(x)=6 what two values for x will give you distance 6 do you know?

  4. anonymous
    • 5 years ago
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    x+6 = 0 --> x=-6 -x-6 = 0 ---> x=-6

  5. myininaya
    • 5 years ago
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    how far is -6 away from 0? how far is 6 away from 0?

  6. myininaya
    • 5 years ago
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    they are both six units from 0

  7. myininaya
    • 5 years ago
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    abs(x)=6 has two solutions x=6 and x=-6 just like we found 2 solutions above but these problems could get trickier along the way and sometimes it will fail to have two solutions so you should begin checking to get in the practice of doing so

  8. myininaya
    • 5 years ago
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    so let's check the above one: we got x=0 and x=-12 lets see if x=0 works plug it into the original equation abs(0+6)-4=2 abs(6)-4=2 6-4=2 2=2 so we got the samething on both sides so x=0 checks out how about x=-12 abs(-12+6)-4=2 abs(-6)-4=2 6-4=2 2=2 so x=-12 checks out

  9. myininaya
    • 5 years ago
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    any questions?

  10. anonymous
    • 5 years ago
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    OK! That makes perfect sense once you broke it down for me!! Thank you both so very much :)

  11. myininaya
    • 5 years ago
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    u r welcome

  12. anonymous
    • 5 years ago
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    Really it's simply a matter of: \[|x+6| - 4 = 2 \implies |x+6| =6 \]\[\implies x + 6 = 6 \text{ and } x+ 6 = -6\] \[\implies x = 12 \text{ and } x = 0\] are solutions.

  13. myininaya
    • 5 years ago
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    no polpak i already won

  14. myininaya
    • 5 years ago
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    lol

  15. anonymous
    • 5 years ago
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    lol. I have another one similar to that, think you could help? \[3x-1\le 7\]

  16. myininaya
    • 5 years ago
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    and he meant x=-12 not 12

  17. anonymous
    • 5 years ago
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    Yes, whoops.

  18. anonymous
    • 5 years ago
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    Certainly, though this one doesn't involve absolute values.

  19. myininaya
    • 5 years ago
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    add the 1 to both sides

  20. myininaya
    • 5 years ago
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    what do you get after you do that?

  21. anonymous
    • 5 years ago
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    \[3x \le8\]

  22. anonymous
    • 5 years ago
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    and when you divide both sides by 3?

  23. myininaya
    • 5 years ago
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    omg gj

  24. myininaya
    • 5 years ago
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    3/3=1 so 3x/3=x so we have x<=8/3

  25. anonymous
    • 5 years ago
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    good...got the same answer!!! Thanks.

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