Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Rearranging Equations

  1. May 20, 2012 #1
    For some reason I have always had problems with rearranging equations, I have no idea how I have got so far in life without knowing how to, so iv been teaching myself.

    Ita extremely simple as well, and thats why i get so worked up about them

    (x-400)/(1000-400)=0.5623

    I know x is 737 I just don't know how to get to it.

    Any help is appreciated

    Rob
     
  2. jcsd
  3. May 20, 2012 #2
    (x-400)/(600)=0.5623
    x-400=0.5623(600)
    x=0.5623(600)+400
    from there it's arithmetic
    x=737.38~737
     
  4. May 21, 2012 #3
    okay, I'll give you a quick lesson on the real numbers!
    Here are four 'axioms' things that we take as true
    1. For any non zero real number, a, there exists another real number [itex]\frac{1}{a}[/itex] such that [itex]a * \frac{1}{a} = 1[/itex]
    2. For any real number, b, there exists another real number -b such that b +(-b) = 0
    3. Operations in the real numbers commute (this means that a * b = b * a and that a + b = b + a)
    4. For any real number c, c*1 = c and c + 0 = c

    We'll use these to help us solve this problem

    (x-400)/(1000-400)=0.5623

    This is the same as saying
    [itex](x-400) * \frac{1}{(1000-400)} = 0.5623[/itex]

    We shall first simplify the things in the brakets by doing 1000-400 = 600 to get
    [itex](x-400) * \frac{1}{600} = 0.5623[/itex]

    Next we shall invoke axiom 1 to state that there exists a number such that [itex]\frac{1}{600} * a = 1[/itex] and we can easily see that a must be 600 (to see this use axiom 3 and 1)
    We shall then multiply both sides by 600 (we must perform the same operations to both sides to keep the equality)

    [itex](x-400) * \frac{1}{600} * 600 = 0.5623 * 600 [/itex]

    Using axiom 1

    [itex](x-400) * 1 = 0.5623 * 600 [/itex]

    Using axiom 4

    [itex]x-400 = 0.5623 * 600[/itex]

    Using axiom 2 we find that there exists a number, a, such that -400 + a = 0, we can see that a must be 400 again, so adding 400 to both sides

    [itex]x - 400 + 400 = 0.5623 * 600 + 400[/itex]

    Using axiom 2 to state 400 + (-400) = 0

    [itex] x + 0 = 0.5623 * 600 + 400[/itex]

    Using axiom 4

    [itex] x = 0.5623 * 600 + 400[/itex]

    Does this help?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Rearranging Equations
  1. Rearranging Formulae (Replies: 4)

  2. Simultaneous Equations (Replies: 2)

  3. Help with equations (Replies: 2)

Loading...