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R00nnYBraiNsbiG

  • 2 years ago

-3|x-2|+10=12 x = 1 and x = 5 x = −1 and x = −5 x = −9 and x = 3 No Solution

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  1. R00nnYBraiNsbiG
    • 2 years ago
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    @AravindG HELP ME PLEASE STEP BY STEP

  2. electrokid
    • 2 years ago
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    \[-3|x-2|=2\] now we square this.. the only way to get rid of the absoute sign is to square it

  3. electrokid
    • 2 years ago
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    or make two equations out of it.

  4. R00nnYBraiNsbiG
    • 2 years ago
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    ok wait spuare the hole thing

  5. electrokid
    • 2 years ago
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    yes see the above simplified orm

  6. electrokid
    • 2 years ago
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    \[\left[-3|x-2|\right]^2=2^2\]

  7. R00nnYBraiNsbiG
    • 2 years ago
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    ok wat about the + 10

  8. electrokid
    • 2 years ago
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    I subtracted it from the two sides

  9. electrokid
    • 2 years ago
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    notice that the right side became 12-10=2

  10. R00nnYBraiNsbiG
    • 2 years ago
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    where did u get the 12 frm

  11. R00nnYBraiNsbiG
    • 2 years ago
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    @electrokid

  12. R00nnYBraiNsbiG
    • 2 years ago
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    where did u get the 12 from

  13. electrokid
    • 2 years ago
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    \[-3|x-2|+10=12\qquad\text{....given}\\ \qquad\qquad-10\quad-10 \]

  14. R00nnYBraiNsbiG
    • 2 years ago
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    ok srry im just learning this ok and then gives u this [−3|x−2|]^2=2^2

  15. electrokid
    • 2 years ago
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    that is ok. well, this first gives \[-3|x-2|=2\] so, we the square it like you just wrote above

  16. R00nnYBraiNsbiG
    • 2 years ago
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    yes

  17. electrokid
    • 2 years ago
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    \[(-3)^2(x-2)^2=(2^2)\] notice that the absolute sign has disappeared

  18. R00nnYBraiNsbiG
    • 2 years ago
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    so 9*2x-4=4

  19. electrokid
    • 2 years ago
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    or to avoid squaring, you can remove the abolute sign in two ways...... \[-3|x-2|=2\implies|x-2|=-{3\over2}\]

  20. R00nnYBraiNsbiG
    • 2 years ago
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    how did u get 3/2

  21. electrokid
    • 2 years ago
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    my bad... \[\Large{|x-2|=\color{red}{-}{2\over3}}\]

  22. R00nnYBraiNsbiG
    • 2 years ago
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    ooh its ok but how did u get that

  23. electrokid
    • 2 years ago
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    divide the two sides by "3"

  24. R00nnYBraiNsbiG
    • 2 years ago
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    ok

  25. electrokid
    • 2 years ago
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    \[{-3|x-2|\over-3}={2\over-3}\]

  26. electrokid
    • 2 years ago
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    this gives the above form.. now, by definition of ABSOLUTE value, can it ever become negative?

  27. R00nnYBraiNsbiG
    • 2 years ago
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    HEY STOP STOP STOP I WROTE THE PROBLEM DWN WRONG SRRY THIS IS THE PROBLEM −3|2x + 6| = −12

  28. electrokid
    • 2 years ago
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    ok... you mean no "10" in there?

  29. R00nnYBraiNsbiG
    • 2 years ago
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    yea

  30. electrokid
    • 2 years ago
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    this is so much different than what you first asked for

  31. electrokid
    • 2 years ago
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    ok.. proceeding similarly, get the absolute quantity on its own...

  32. R00nnYBraiNsbiG
    • 2 years ago
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    ik b/c its 2 differnt problems in one

  33. electrokid
    • 2 years ago
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    \[\Large{-3|2x-6|=-12\\\text{divide both sides by -3}\\ |2x-6|=4\\\text{to get rid of absolute sign, we get two possible answers}\\\;\\ 2x-6=4\qquad{\rm AND}\qquad2x-6=-4\\ 2x=4+6\qquad\qquad\qquad2x=-4+6\\ 2x=10\qquad\qquad\qquad\quad2x=2\\ \boxed{x=5}\qquad\qquad\qquad\quad\boxed{x=1}} \]

  34. electrokid
    • 2 years ago
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    check, plug in "x=" those numbers in the given problem on the left side. That should give you the right side.

  35. R00nnYBraiNsbiG
    • 2 years ago
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    thanks

  36. electrokid
    • 2 years ago
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    did you understand?

  37. R00nnYBraiNsbiG
    • 2 years ago
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    yes

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