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Math Help - absolute value..2 different answer

  1. #1
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    Exclamation absolute value..2 different answer

    absolute value

    I getting a different answer...don't know why

    |3-4x|≥2

    what i did was=====> i made it in to 2 parts ===>3 - 4x ≥ 2 and 3 - 4x ≥-2

    my final answer that i got is
    1/4≥x (first part) and (second part) 5/4 ≥ x

    but the teacher got
    1/4≥x and 5/4 ≤ x
    why did the sign change for the last one? i dont get it
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  2. #2
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    Quote Originally Posted by Candy101 View Post
    absolute value

    I getting a different answer...don't know why

    |3-4x|≥2

    what i did was=====> i made it in to 2 parts ===>3 - 4x ≥ 2 and 3 - 4x ≥-2

    my final answer that i got is
    1/4≥x (first part) and (second part) 5/4 ≥ x

    but the teacher got
    1/4≥x and 5/4 ≤ x
    why did the sign change for the last one? i dont get it
    Redo the second problem: 3-4x≥-2, first subtract 3: 3-3-4x≥-5 = -4x≥-5
    then, divide by NEGATIVE 4 = 5/4≤ x (or you could say x≥5/4). The reason the sign changed is because you divided by a NEGATIVE number. Any time you divide by a negative number, the direction of the sign changes.
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  3. #3
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    assuming you get that:

    2 \leq |3x - 4|
    \rightarrow 2 \leq (3x - 4 ) and 2 \leq -(3x - 4)

    Using the second inequality and multiplying both sides by -1

    2 \leq -(3x -4) \rightarrow -2 \geq (3x-4)

    Note: When you multiply both sides of an inequality by -1, you have to flip the direction of inequality

    For example: 1 < 2 \rightarrow -1 > -2

    So -2 \geq (3x -4) \rightarrow \frac{5}{4} \leq x
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  4. #4
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    Quote Originally Posted by Candy101 View Post
    absolute value

    I getting a different answer...don't know why

    |3-4x|≥2

    what i did was=====> i made it in to 2 parts ===>3 - 4x ≥ 2 and 3 - 4x ≥-2

    my final answer that i got is
    1/4≥x (first part) and (second part) 5/4 ≥ x

    but the teacher got
    1/4≥x and 5/4 ≤ x
    why did the sign change for the last one? i dont get it
    Hi Candy101,

    |3-4x| \le 2

    Understand this basic principal:

    If |a| > b, then a > b or a < -b

    Therefore,

    3-4x \ge 2 \ \ or \ \ 3-4x \le -2

    -4x \ge -1 \ \ or \ \ -4x \le -5

    x \le \frac{1}{4} \ \ or \ \ x \ge \frac{5}{4}
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  5. #5
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    how to graph absolute value

    how to graph this

    y=3|x+2|-9

    it says graph: vertex and intercepts

    by the way how do u find the vertex of any problem?

    thanks
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  6. #6
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    Quote Originally Posted by Candy101 View Post
    how to graph this

    y=3|x+2|-9

    it says graph: vertex and intercepts

    by the way how do u find the vertex of any problem?

    thanks
    HI

    you can start by sketching y=3|x+2| first . Find its intercepts

    when x=0 , y=6

    when y=0 , x=-2

    so there will be a line passing through 6 to -2 , then the line is reflected since there is a modulus , it cant take negative values of y .

    After this , shift the graph down for 9 units .
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  7. #7
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    Quote Originally Posted by mathaddict View Post
    HI

    you can start by sketching y=3|x+2| first . Find its intercepts

    when x=0 , y=6

    when y=0 , x=-2

    so there will be a line passing through 6 to -2 , then the line is reflected since there is a modulus , it cant take negative values of y .

    After this , shift the graph down for 9 units .
    how did you get 6 and -2?
    can u please show or explain ur steps?
    thanks,
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  8. #8
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    Quote Originally Posted by Candy101 View Post
    how did you get 6 and -2?
    can u please show or explain ur steps?
    thanks,
    Put x and y =0 respectively to get the intercepts (points where the line cuts the x and y axis )
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