Is 1.252525252525 repeating irrational
1 answer:
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Since x can't be zero (it sits at the denominator of the left hand side), let's split cases:
If x is positive
It this case, we can multiply both sides by x without changing the inequality sign:
But since we're assuming that x is positive, we can only accept the numbers between 0 and 1.
If x is negative
It this case, in order to multiply both sides by x we have to change the inequality sign:
But since we're assuming that x is negative, we can only accept the numbers which are smaller than -1.
So, putting all the pieces together, we have that the solution is given by the following interval: