Anonymous
Anonymous asked in Science & MathematicsMathematics · 1 decade ago

inequalities and abs. value?

could someone please walk me through how to do a problem like this:

3<|3x-4|<12

3 Answers

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  • Anonymous
    1 decade ago
    Best Answer

    3<|3x-4|<12

    |3x -4| = 3x -4 when x > 4/3

    |3x -4| = -(3x -4) when x < 4/3

    3<|3x-4|<12

    a) x > 4/3 , we solve

    3< 3x-4 <12

    let's add 4 to all term of the inequalities

    3 +4 < 3x < 12 +4

    7< 3x < 16

    divide all term by 3 to get

    7/3 < x < 16/3

    b) x <4/3

    we solve

    3< -3x+4 <12

    let's add -4 to all term of the inequalities

    3 -4 < -3x < 12 -4

    -1 < -3x < 8

    let's divide by (-3) all terms (dividing by a negative number changes all < to > )

    1/3 > x > -8/3

    Summary:

    a) x > 4/3

    7/3 < x < 16/3 ---> solution domain1 =

    b) x <4/3

    1/3 > x > -8/3

    -8/3 < x < 1/3 = solution domain2

    ******************

  • 1 decade ago

    Break off the absolute symbol by breaking the inequality into its two parts. For example, |x| > 5 turns into x > 5 and x < -5

    So:

    3 < (3x -4) < 12

    or

    -3 > (3x-4) > -12

    Add 4 to all sides

    7 < 3x < 16

    or

    1 > 3x > -8

    Divide by 3 to all sides. If it were -3x, you'd have to flip the inequality symbol again, but here it stays the same

    7/3 < x < 16/3

    or

    1/3 > x > -8/3

  • cidyah
    Lv 7
    1 decade ago

    3<|3x-4|<12

    case 1: 3x-4 >0

    |3x-4| = 3x-4

    3x-4 < 12

    3x < 16

    x < 16/3

    3x-4 >3

    3x > 7

    x > 7/3

    7/3 < x < 16/3 --- (1)

    case 2:

    3x-4 < 0

    3x-4 =-(3x-4)

    =-3x+4

    -3x+4 < 12

    -3x < -8

    3x > 8

    x > 8/3

    -3x+4 > 3

    -3x > -1

    3x < 1

    x < 1/3

    7/3 < x < 16/3 -- (1)

    8/3 < x < 1/3 --- (2)

    Draw a line and see where x lies based on (1) and (2). That is your solution.

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