stewartlife wrote:
Hi all,
If I have an inequality: (a/b) < 0
Why can't I derive: a < 0(b) therefore a < 0?
But in equation (a/b) = 0, I can say a = 0, right?
Please help to explain. Thanks!
Think about it this way:
a/b < 0 implies a/b is negative.
When will a fraction be negative? When either numerator or denominator is negative and the other is positive.
So if a/b is negative, it means either a or b (but not both) is negative.
If
a = 4, b = -5, a/b = -(\frac{4}{5}) (negative)
If
a = -4, b = 5, a/b = -(\frac{4}{5}) (negative)
So given a/b < 0, all you can say is that one and only one of a and b is negative and the other is positive. You cannot say which one is negative and which is positive.
On the other hand, a/b = 0 only when a = 0. If b = 0, then a/b is not defined.
You can cross multiply, i.e. take b to the other side, when dealing with equations.
While dealing with inequalities, you cannot cross multiply until and unless you know the sign of the variable. If you know that b is positive, then you can take it to the other side. If you know that b is negative, then you can take it to the other side but you need to flip the inequality sign. If you do not know the sign of b, you cannot take it to the other side.
I would suggest you to check out our Algebra book for a detailed discussion on basics of Inequalities.
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Karishma
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