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Math Help - Absolute Value Issues

  1. #1
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    Absolute Value Issues

    I'm having some trouble working out some questions for absolute values:

    |4y - 7| = |3y - 2|


    1 / |y-2| is greater than or equal to 3


    |5y - 2| = |3x + 4|
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  2. #2
    Senior Member DivideBy0's Avatar
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    Quote Originally Posted by Ogsta101 View Post
    I'm having some trouble working out some questions for absolute values:

    |4y - 7| = |3y - 2|


    1 / |y-2| is greater than or equal to 3


    |5y - 2| = |3x + 4|
    Question 2

    \frac{1}{|y-2|}\geq 3

    Since the LHS must be positive, we can reciprocate both sides, reversing the inequality sign:

    |y-2| \leq \frac{1}{3}

    \Rightarrow -\frac{1}{3}\leq y-2\leq \frac{1}{3}

    \Rightarrow \frac{5}{3} \leq y \leq \frac{7}{3}
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  3. #3
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Ogsta101 View Post
    I'm having some trouble working out some questions for absolute values:

    |4y - 7| = |3y - 2|
    bearing in mind the definition of absolute values (look this up of you don't know), we realize the solution will be given by:

    4y - 7 = \pm (3y - 2)

    so we have 4y - 7 = 3y - 2

    or

    4y - 7 = 2 - 3y

    solve those for your two solutions.

    |5y - 2| = |3x + 4|
    what do you want to do here? you have two unknowns. which do you want to solve for...? is this a typo? in any case, try a similar method to what i did above
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  4. #4
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    Just square both sides to get right rid of absolute values. Then see which solutions to the quadradic satisfy the original equation.
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  5. #5
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    Quote Originally Posted by Ogsta101 View Post
    I'm having some trouble working out some questions for absolute values:
    |4y - 7| = |3y - 2|
    1 / |y-2| is greater than or equal to 3
    |5y - 2| = |3x + 4|
    Absolute value is when anything in between the || is going to end up in the positive state of a number. Your first question states :
    |4y - 7| = |3y - 2|
    so when you look at it, it should be like this:
    4y + 7 = 3y + 2
    4y-3y=-7+2
    If you are supposed to solve the answer would be:
    y= -5
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  6. #6
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by starrynight View Post
    Absolute value is when anything in between the || is going to end up in the positive state of a number. Your first question states :
    |4y - 7| = |3y - 2|
    so when you look at it, it should be like this:
    4y + 7 = 3y + 2
    4y-3y=-7+2
    If you are supposed to solve the answer would be:
    y= -5
    you seem to be confused about absolute values. it does not mean you just change all the signs to positive. first of all, there are two answers, second of all, none of them is the answer you gave (plug it into the equation and you'll see it is wrong). do as i did or what TPH did (i prefer his method, and it is more standard than mine) to solve the problem. and look up the definition of what it means to take absolute values
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