The reciprocal of n must be less than –10
Solution:
Given n denotes a number to the left of 0 means n < 0.
Square of n is less than [tex]\frac{1}{100}[/tex] means [tex]n^2<\frac{1}{100}[/tex].
Therefore, we have [tex]n<0[/tex] and [tex]n^2<\frac{1}{100}[/tex].
⇒ [tex]n^2<\frac{1}{100}[/tex]
Taking square root on both sides, we get
⇒ [tex]n<\± \frac{1}{10}[/tex]
⇒[tex]\frac{-1}{10}<n<\frac{1}{10}[/tex]
⇒ But we know that n < 0, so [tex]n<\frac{1}{10}[/tex] false.
It should be [tex]\frac{-1}{10}<n[/tex].
To equal the expression, multiply both sides of the equation by –10n.
⇒ [tex]-\frac{1}{10} \times\frac{-10}{n}>n \times\frac{-10}{n}[/tex] (symbol < changed to > when multiply by minus)
⇒ [tex]\frac{1}{n}>-10[/tex]
Hence, the reciprocal of n must be less than –10.
