Just a series of quick questions about equations. (I'm writing the test in several days. These are my remaining uncertainties on this topic. Please help.)
1) Is it true that you cannot divide variable in an equation unless you know for sure that it is not zero? (<= Is this even a correct rule?)
a) Given the expression X=Y can you simplify to => X/Y=1? or does it have to be X-Y=0?
b) However the opposite can be done: If you have X/Y=1 then => X=Y?
c) Ex: W*X*Y*Z does NOT equal Zero, Is W/X=Y/Z?
1) W/Z=Y/X
2) WZ=YX
(OA is A) Since WXYZ cannot be equal to zero how come you cant divide X on one side and Z on the other? Can a tutor expand on this concept to give us some key takeaways from these problems. (If you test numbers, 2 is definitely inconclusive) What's the mathematical concept here? I'm so used to cross-multiplying and dividing variables in equations especially on ratio type problems and have taken granted these operations. What is the fundamental math principles that allows you to divide in many problems [rates/work problems] but cannot in some such as this one.)
2) Multi-solution problems (Absolute and quadratics)
a) Do you have to test the values everytime to make sure its a real solution?
b) Is there a way to tell if you should test or not? (I heard that if the expression is a square-root or absolute value, you have to test)
Thanks.
1) Is it true that you cannot divide variable in an equation unless you know for sure that it is not zero? (<= Is this even a correct rule?)
a) Given the expression X=Y can you simplify to => X/Y=1? or does it have to be X-Y=0?
b) However the opposite can be done: If you have X/Y=1 then => X=Y?
c) Ex: W*X*Y*Z does NOT equal Zero, Is W/X=Y/Z?
1) W/Z=Y/X
2) WZ=YX
(OA is A) Since WXYZ cannot be equal to zero how come you cant divide X on one side and Z on the other? Can a tutor expand on this concept to give us some key takeaways from these problems. (If you test numbers, 2 is definitely inconclusive) What's the mathematical concept here? I'm so used to cross-multiplying and dividing variables in equations especially on ratio type problems and have taken granted these operations. What is the fundamental math principles that allows you to divide in many problems [rates/work problems] but cannot in some such as this one.)
2) Multi-solution problems (Absolute and quadratics)
a) Do you have to test the values everytime to make sure its a real solution?
b) Is there a way to tell if you should test or not? (I heard that if the expression is a square-root or absolute value, you have to test)
Thanks.
