|-2x|= |2x| why?

Discussion in 'Computer Support' started by Solar^, Dec 3, 2005.

  1. Solar^

    Solar^ Guest

    Greetings Group,
    Thought some of you programmer-mathematicians might be able to answer this
    question - why doe |-2x| = |2x| and not just 2x? Studying for a math final
    is why I want to know.
    Regards,
    Solar^
     
    Solar^, Dec 3, 2005
    #1
    1. Advertisements

  2. Solar^

    James Guest

    Because any double negatives multiplied together gives a positive answer.

    if i recall my maths correctly:

    negative multiplied or divided by a negative = positive
    one negative multiplied or divided by a positive = negative

    Ohh watch me get this one wrong ;)
     
    James, Dec 3, 2005
    #2
    1. Advertisements

  3. Solar^

    philo Guest


    because -2x does NOT = 2x

    but the absolute value of -2x *does* equal the absolute value of 2x

    if you have gotten to your finals...
    you should know what "absolute value" means by now !
     
    philo, Dec 3, 2005
    #3
  4. Solar^

    Solar^ Guest

    Ok, Philo,
    If x were 4, then |-2*4| = 8 -> 2*4 0r just plain 2x and |2x| seems a
    little redundant since x is already a positive number. If it were a
    negative number then |-2*-4| <> 2*-4 (2x) but rather |2x| ok.. got it
    thanks!
     
    Solar^, Dec 3, 2005
    #4
  5. Solar^

    DC Guest

    Not exactly.
    This is true, but...
    ....you didn't answer his question correctly. }:O) See philo's answer.
     
    DC, Dec 3, 2005
    #5
  6. Solar^

    Fred Guest

    If x is negative then 2x does not equal to |2x|.
     
    Fred, Dec 3, 2005
    #6
  7. Solar^

    Mike Easter Guest

    I think it is useful to make a statement of the equation, or rather the
    original question.

    Why does the absolute value of -2x equal the absolute value of 2x, and
    not just '2x'?

    And, before we begin to answer the question, we remember something
    important about absolute values and variables.

    When you are dealing with a variable's value, you don't know the sign of
    the value; that is, you don't know whether the variable x represents a
    postive or negative value. So, if x is a negative value, the absolute
    value of it changes the sign of the value, whereas if x is a positive
    value, it doesn't.

    Now back to our statement.

    If x is a positive value, |-2x| = |2x| *AND* 2x *BUT*

    If x is a negative value, [-2x| = |2x| *BUT NOT* 2x *because*

    in the case of x being a negative value, 2x would also, which the
    absolute values are not.
     
    Mike Easter, Dec 3, 2005
    #7
  8. Solar^

    Mike Easter Guest

    Short form:

    Because 2x can have a negative value, which the absolutes can't.

    But, that answer doesn't seem to have a 'long enough' "why?" wrapped
    around it.
     
    Mike Easter, Dec 4, 2005
    #8
  9. Solar^

    philo Guest

    good!

    BTW: it took me quite a few tries and many years to get anywhere in math!!!!
     
    philo, Dec 4, 2005
    #9
  10. Solar^

    john60 Guest

    I am not sure for the answer, this is what I remember:

    |-2x| = |2x| is the same as |-a| = |a| ...and it's not an equation,
    it's the definition of absolute value

    No matter if x is negetive or positive, |-2x| = |2x|

    Assume x = 4

    |-2 * 4| = |2 * 4|
    |-8| = |8|

    since |8|=8 and |-8|=8|, then it indeed |-8| = |8|

    Assume x = -3

    |-2 * - 3| = | 2 * -3|
    |6| = |-6|

    since |6|=6 and |-6|=6, then indeed |-6| = |6|

    Note that:

    + * + = +
    + * - = -
    - * - = +

    + / + = +
    + / - = -
    - / + = -
    - / - = -
     
    john60, Dec 4, 2005
    #10
  11. Howdy!

    Because X might be a negative number.

    If x = -4, then -2x = 8, but 2x = -8.

    But the absolute value of both are 8.

    RwP
     
    Ralph Wade Phillips, Dec 4, 2005
    #11
  12. Solar^

    mdp Guest

    Because the solution must be good for all x and for the case when x is
    negative

    |-2x| = |2x| does not equal 2x
     
    mdp, Dec 4, 2005
    #12
    1. Advertisements

Ask a Question

Want to reply to this thread or ask your own question?

You'll need to choose a username for the site, which only take a couple of moments (here). After that, you can post your question and our members will help you out.