You can put this solution on YOUR website! multiplication principle is defined here. http://www.jamesbrennan.org/algebra/intro%20to%20algebra/multiplication_principle.htm
your problem is:
-4.6b = 16.56
divide both sides of this equation by -4.6 to get:
b = 16.56 / -4.6 = -3.6
dividing by -4.6 is the same as multiplying by 1/-4.6 so the multiplication principle holds even though i used division.
-4.6 * 1/-4.6 = 1
16.56 * 1/-4.6 = -3.6
your equation becomes 1*b = -3.6 which becomes b = -3.6
the principle is:
you can multiply both sides of the equation by the same factor and the equality will be preserved.
likewise you can divide both sides of the equation by the same factor and the equality will be preserved.
in both of these, the factor should not be 0.
in the division it is clearly not allowed.
in the multiplication, the 0 will make the x disappears which changes the equation so that x can be any value which would not be correct.
example:
x/15 = 30
multiply both sides of this equation by 15 to get x = 15*30 = 450.
multiply both sides of this equation by 30 to get 2x = 900
multiply both sides of this equation by 0 to get 0x = 0 which becomes 0 = 0
the x falls out of the equation which means that x can be any value.
this is not allowed because it changes the equation to something it was not before.
any other value of x will find the correct value of x.
when you multiplied both sides by 15 you got x = 450 directly.
when you multiplied both sides by 30 you got 2x = 900 which led you to x = 450 after you divided both sides by 2.
multiplying by 0 led you nowhere which is why 0 is not allowed as a multiplication factor.
