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algebra

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could you please check my answer and show me correct way . thanks for your help

solve the equation if pssible
-3|6n-2| +5 = 8
note:: 6n-2 is abolute value
6n-2 is positive
-3|6n-2| + 5 = 8
|6n-2| = 6
6n - 2 = 6
6n - 2 +2 = 6 + 2 divide by 6
n = 8/6

6n-2 negative
-3|6n-2|+ 5 = -8
|6n-2|+ 2 = -8
|6n-2| = -10
6n-2 +2 = -10 + 2
6n = -8 divide by 6
n = -8/6

  • algebra -

    -3|6n-2| +5 = 8

    case I: absolute value is positive. thus,
    -3(6n-2) + 5 = 8
    -3(6n-2) = 8 - 5
    -3(6n-2) = 3
    6n - 2 = -1
    6n = 1
    n = 1/6

    case II: absolute value is negative. thus,
    -3[-(6n-2)] + 5 = 8
    3(6n-2) + 5 = 8
    3(6n-2) = 3
    6n - 2 = 1
    6n = 3
    n = 1/2

    NOTE: these are not yet the answers. we must check if they satisfy the original equation by substituting each:
    n = 1/6:
    -3|6n-2| + 5 = 8
    -3|6*1/6 - 2| + 5 = 8
    -3|1-2| + 5 = 8
    -3|-1| + 5 = 8
    -3(1) + 5 = 8
    -3 + 5 = 8
    2 = 8 (this cannot be, thus n = 1/6 is not a solution)

    n = 1/2:
    -3|6n-2| + 5 = 8
    -3|6*1/2 - 2| + 5 = 8
    -3|3 - 2| + 5 = 8
    -3|1| + 5 = 8
    -3 + 5 = 8
    2 = 8 (this cannot be, thus n = 1/6 is not a solution)

    Therefore, no solution exists.

    If you have questions, don't hesitate to ask. :)
    Hope this helps~ :)

  • algebra -

    thank you very much Jai for taking the time to help me ann

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