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8 February, 02:03

Solve the absolute value equation and check for extraneous solutions. 9|9-8x|=2x+3 show work

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  1. 8 February, 04:38
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    For |a|=b, solve a=b and a=-b

    so

    9|9-8x|=2x+3

    divide both sides by 9

    |9-8x|=2/9x+1/3

    so

    9-8x=2/9x+1/3 or 9-8x = (-2/9x+1/3)

    multiply both sides by 9

    81-72x=2x+3 or 81-72x=-2x-3

    add 72x to both sides

    81=74x+3 or 81=70x-3

    for the first one, minus 3 both sides, 2nd one add 3 both sides

    78=74x or 84=70x

    divide both sides by 74 or 70, (first and 2nd equations respectivly)

    78/74=x or 84/70=x

    39/37=x or 6/5=x

    if we check, they both yeild true statements

    x=39/37 or 6/5
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