2 Inequalities with Abs. Value - written in interval notation :)?

1. | 4 - 3x | + 1/2 < -2

written in interval notation

2. |3 - 2x | - 8 >= 1

written in interval notation

thanks!

3 Answers

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  • 1 decade ago
    Best Answer

    Hi,

    1. | 4 - 3x | + 1/2 < -2

    | 4 - 3x | < -2½

    This is looking for the values of x such that the absolute value of 4 - 3x is less than -2½. Since an absolute value is nonnegative, it is NEVER less than a negative number. For this problem there is no solution, so the answer is Ø.

    2. |3 - 2x | - 8 ≥ 1

    |3 - 2x | ≥ 9

    3 - 2x ≥ 9 or 3 - 2x ≤ -9

    -2x ≥ 6 or -2x ≤ -12

    x ≤ -3 or x ≥ 6

    The answer is (-∞,-3) U (6,∞)

    I hope that helps!! :-)

  • 1 decade ago

    |a|<b means -b<a<b

    |a|>b means a<-b or a>b

    so:

    1. | 4 - 3x | + 1/2 < -2

    |4-3x|<-5/2. I think it is impossible because |a| means the absolute value of a, so the things that are between the"|" is always positive.

    2. |3 - 2x | - 8 >= 1

    |3-2x|>=9

    -9>=3-2x or 3-2x>=9

    -12>=-2x or -6>=2x

    x>=6 or x<=-3

  • Anonymous
    1 decade ago

    1.

    | 4 - 3x | + 1/2 < -2

    | 4 - 3x | + 1/2 - 1/2 < -2 -1/2

    | 4 - 3x | < -2,5

    S = { }

    There is no such number whose absolute value is negative.

    2.

    | 3 - 2x | - 8 >= 1

    | 3 - 2x | - 8 + 8 >= 1 + 8

    | 3 - 2x | >= 9

    EITHER;

    3 - 2x >= 9

    3 - 2x - 3 >= 9 - 3

    -2x >= 6

    -1/2*(-2x) <= -1/2*6

    x <= -3

    OR;

    3 - 2x <= -9

    3 - 2x - 3 <= -9 - 3

    -2x <= -12

    -1/2*(-2x) >= -1/2*(-12)

    x >= 6

    S= (-∞,-3] U [6,∞)

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