Question 542518: If I have the following problem:
x = 3.5 X 10 to the 18th power; y = 3.0 x 10 to the 8th power; and I'm solving for z,
my formula is: x = y/z
3.5 x 10 to the 18th = 3.0 x 10 to the 8th/z,
and the solution comes out:
z = 3.0 x 10 to the 8th/3.5 X 10 to the 18th
Okay, here's the question. What property or rule is at play here that they can take 1/z and make it z and flip the other two?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! if you multiply both sides of an equation by the same amount, then the equality of the equation remains the same.
you have x = 3.5 * 10^18
you have y = 3.0 * 10^8
you have:
3.5 * 10^18 = (3.0 * 10^8) / z
since x = 3.5 * 10^18 and y = 3.0 * 10^8, then this is the same as:
x = y / z
if you multiply both sides of this equation by z, you will get:
x*z = y
if you divide both sides of this equation by x, you will get:
z = y / x
the rule is that you can multiply or divide both sides of the same equation by the same amount and the equality is preserved.
the general rule for solving equations is:
in order to preserve the equality, whatever you do to one side of the equation you have to do to the other.
this means:
you multiply both sides of the equation by the same amount.
you divide both sides of the equation by the same amount.
you take the root of both sides of the equation by the same power.
you raise both sides of the equation by the same power.
some examples:
5 = 5
5*5 = 5*5
5/5 = 5/5
5^2 = 5^2
sqrt(5) = sqrt(5)
as long as you perform the same operation on both sides of the equation then the equality is preserved.
assume x = 4 and y = 20 and z = 5
the equation of x = y / z becomes:
4 = 20 / 5
now multiply both sides of this equation by 5 to get:
4*5 = 20
this equation is true to that part is ok.
now divide both sides of this equation by 4 to get:
5 = 20 / 4
this equation is true so that part is ok.
we started with x = 4 and y = 20 and z = 5
substituting letters for values in the last equation gets us:
z = y / x
we started with x = y / z and wound up with z = y / x
it's the "whatever you do to one side of the equation you have to do to the other side of the equation to preserve the equality" rule that allows this to happen.
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