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Show all steps solve the equation check for extraneous solution 9|9-8 x|=2x+3

  • algebra -

    9|9-8 x|=2x+3 , x ≥ -3/2
    |9-8 x|=(2x+3)/9

    9-8x = (2x+3)/9
    81 - 72x = 2x+3
    -74x = -78
    x = -78/-74
    x = 39/37
    or
    9-8x = -(2x+3)/9
    81 - 72x = -2x - 3
    -70x = -84
    x = 87/70 = 6/5

    check:
    if x = 6/5
    LS = 9|9-8(6/5)|
    = 27/5
    RS = 2(6/5)+3
    = 27/5 , so x = 6/5

    if x = 39/37
    LS = 9|9-8(39/37)|
    = 189/37
    RS = 2(39/37) + 3 = 189/37 , so x = 39/37

  • algebra -

    so yes?

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