1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Infinate Value Problems

  1. Apr 11, 2005 #1

    I was wondering if anyone could help me with these infinate value questions that I really dont get... :uhh:

    stuff like this:

    |2x+4| = 16


    |10x| + 5 = 40

    (i made these questions off the top of my head, so they might not work out properly and nicely)

    Thanks :smile:
  2. jcsd
  3. Apr 11, 2005 #2

    matt grime

    User Avatar
    Science Advisor
    Homework Helper

    Are you only looking for answers where x is a real number? Since there are only at most two answers.

    |y|= r if and only if y=r or y=-r.

    If you're talking abuot C or some other space, just say so and someone will explain what to do there.
  4. Apr 11, 2005 #3


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    Dearly Missed

    You do mean "absolute value", right?
    The way to solve these questions is:
    1) Determine the different x-intervals in which the expression inside a given absolute value signs are positive or negative.
    For example, for your second case we have:
    [tex]10x<0\to{x}<0, 10x\geq0\to{x}\geq0[/tex]
    Hence, you have two distinct regions two consider: x less than 0 and x greater than (or equal to) zero.

    2) See what solutions exist, if any, on each region:
    In your second case:
    Here, 10x<0, so |10x|=-10x.
    Thus, we must check if we have actual solutions satisfying: -10x+5=40
    Rearranging terms, we get [tex]x=-3.5[/tex]
    Since -3.5<0, this represents a true solution, since x must be negative in this region.

    Here, |10x|=10x, thus we must check if we have solutions of: 10x+5=40
    and we see that x=3.5 works.
    Get it?
    If you are to find solutions where you have nummerous addends in the form of absolute values, just split up your analysis in the appropriate manner.
    Last edited: Apr 11, 2005
  5. Apr 11, 2005 #4
    thanks a bunch
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook