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Reexpressing equations

  1. Oct 20, 2012 #1
    I am solving equations for a problem where we must reexpress the equation. I have been given the reexpressed equations, but simply cannot see the steps to quickly change the expression.

    The expressions are below

    1. Q = 12-2P.. it is reexpressed as P = 6-Q/2
    2. Q = 18-P... it is reexpressed as P = 18-Q
    3. Q = 8-p/3...it is reexpressed as P = 24-3Q

    Can anyone tell me the steps to get from the initial equations to the new expressions?

  2. jcsd
  3. Oct 20, 2012 #2


    Staff: Mentor

    We normally say "rewrite". I don't think I've ever seen anyone use "reexpress".

    When you solve an equation for one variable, you get a new equation.
    These are very simple linear equations. Your book must have some examples of solving a linear equation for one variable in terms of another.
  4. Oct 20, 2012 #3


    Staff: Mentor

    After thinking about this "reexpressing" equations terminology, is this terminology used by your instructor or in the textbook? I don't see the point of it in light of the fact that there already is some perfectly good terminology -- equivalent equations.

    In your first example, Q = 12 - 2P and P = 6 - Q/2 are equivalent equations. Any pair of numbers (P, Q) that satisfies the first equation also satisfies the second equation.
  5. Oct 21, 2012 #4
    This was from a textbook.

    We needed to reexpress a demand curve for individuals to attempt to set a new tax rate for each individual.

    I was just more or less trying to find another example of how those equations were rewritten(reexpressed) so I could understand all the steps in the text examples
  6. Oct 21, 2012 #5


    User Avatar
    Homework Helper

    Ok well for the first we have

    Q = 12 - 2P

    and we want to make the variable P the subject (which means have it in the form P = ...)

    So the first thing we do is take away 12 from both sides,

    Q - 12 = 12 - 2P - 12

    and notice that on the right side the 12's cancel, so we can simplify that into

    Q - 12 = -2P

    Now, we have -2 times P, and we want just P, so we can divide by -2 to give

    (Q-12)/(-2) = -2P/(-2)

    And the right side is now obviously just P. But what we want to do is simplify the left side of the equation.

    Well, to do this we have a basic rule of fractions which is


    so what we end up with is

    Q/(-2) -12/(-2) = P

    And since -12/-2 = 12/2 = 6 and Q/-2 = -Q/2 we have

    6 - Q/2 = P

    We can also switch each side of the equality without a problem, so our final answer is

    P = 6 - Q/2
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