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solve the absolute value problem : 3x+|4x+5|=10

  • math -

    In mathematics, the absolute value |a| of a real number a is the numerical value of a without regard to its sign.

    So, for example, the absolute value of 3 is 3, and the absolute value of
    -3 is also 3.


    In this case:


    | 4 x + 5 | = 4 x + 5

    OR

    | 4 x + 5 | = - ( 4 x + 5 ) = - 4 x - 5


    Equation:

    3 x + | 4 x + 5 | = 10

    has two solutions.


    1.)


    3 x + 4 x + 5 = 10

    7 x = 10 - 5

    7 x = 5 Divide both sides with 7

    x = 5 / 7



    2.)


    3 x - ( 4 x + 5 ) = 10

    3 x - 4 x - 5 = 10

    - x = 10 + 5

    - x = 15 Multiply both sides with - 1

    x = - 15

  • math -

    | 4 x + 5 | = 4 x + 5

    | - ( 4 x + 5 ) | = | - 4 x - 5 | = | 4 x + 5 |

  • math -

    More direct way:

    3x+|4x+5|=10
    |4x+5| = 10-3x
    4x+5 = 10-3x OR -4x-5 = 10-3x
    7x = 5 OR -x = 15

    x = 5/7 OR x = -15

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