If I have pi on both sides of an equation, can they cancel each other out?

And what if there is two pi on one side and one in the other.

Examples 10 pi =2 pi * 4 pi x

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  • 8 years ago
    Favorite Answer

    Yes because pi is a # (3.14...) so if you divide by pi on one side of the equal sign, you will have to divide by pi on the other side of the equal sign, however it will only cancel out one of the pi.

    Which will then be 10=2 X 4 pi x

  • Bill G
    Lv 6
    8 years ago

    Ms. D. Answer: Yes and No. First, let me explain the oder of operations for dealing with polynomials.

    You can remember it by :"Please Excuse My Dear Aunt Sally: The P stands for closing everything in Parentheses first. The E stands for closing all values with Exponents next.The M an D stands for doing all Multiplication and Division next (does no matter which order you use: M 1st, D: second or D 1st, M second) . The A and S stand for doing all Adding and Subtraction last. Example: 10 pi =2pi*4pi x. Had it been 10 pi = 6pi -12; We could use a rule of math which says one may add, subtract, multiply, divide, square; take square roots, change signs(+ to -) (- to +) on one side of any equation by any value and THE EQUATION WILL REMAIN CORRECT AS LONG AS ONE DOES THE EXACT SAME THING TO THE OTHER SIDE USING THE EXACT SAME VALUES. By that , we could simply subtract 6pi from both sides of the equation to get 10pi -6pi=6pi-6pi -12 and we get 4pi=-12, and pi (or any other value) =-3. Note: With practtice, you will find shortcuts; however the reasoning is the same.: With 10pi=2pi * 4pi (assuming the * means multiplying) we must complete the multiplication on the right side before we can do any addition or subtracting: 10pi =2pi *4pi=8pi^2

    Now we can subtract 10pi from the left side to get 8pi^2-10pi+C =0; This we could factor to:

    ((4pi+1(2pi-3) =2pi x 4pi-10pi -C(-3) ; 8pi^2-10pi -3=0. This gives us either pi=1/4 or pi = -3/2. Pi=1/4 is not rational; therefore, we are left with pi=-3/2. We plug this in to8 *pi^2-10 pi -3= 0;

    8(-3/2)(-3/2) -10(-3/2)-3=0 8(9/4)-10*(-1/2)-3= 0; 72/4 -30/2-3=0 18-15-3=0; 0=0.Hope this helps. Good luck

  • 8 years ago

    Blueberry is the best! :D

    Source(s): Dessert
  • Moon
    Lv 7
    8 years ago

    10 pi =2 pi * 4 pi x

    10 pi = 8 pi² x

    2 pi (5 = 4 pi x) .............. 2pi common .... eliminated

    5 = 4 pi x

    5/(4pi) = x ................. answer

    you can, if you like, further solve it for numerical value

    x = 1.25/pi

    x = 0.4

    ........... done

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  • 8 years ago

    Because pi is not equal to zero, you are allowed to divide both sides by pi

    10*pi = 2*pi * 4*pi x

    divide both sides by pi

    10*(pi/pi) = 2*(pi/pi) * 4*pi x

    Because pi is not equal to zero, then pi/pi = 1

    10 = 8*pi x

    -----

    Remember that pi is "just a number"

    It may be a special number, but it is still "just a number"

  • 8 years ago

    10*pi = 2*pi*4*pi*x

    Divide through by pi:

    10 = 2*pi*4*x

    10 = 8*pi*x

    x = 10/(8*pi)

    x = 5/(4*pi)

    x = 1.25/pi

    x =~ 0.39788735772973833942220940843129

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