we can't change the inequality when we have -ve nd RHS +ve in reciprocal
I don't understand what you mean by this?
10) If 4/x <1/3, what is the possible range of values for x?
We need to consider 2 cases
You do need to consider 2 cases, but you only need to spend any time on one of them. We know:
4/x < 1/3
This will clearly be true if x is negative, since then the left side is negative, and the right side is positive, and negative numbers are certainly smaller than positive ones. So whenever x < 0, the inequality is true.
Now for the second case: if x > 0, we can multiply both sides by x without needing to worry about reversing the inequality:
4 < x/3
12 < x
So either x < 0, or 12 < x.
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