If n denotes a number to the left of 0 on the number line such that the square of n is less than , then the reciprocal of n must be

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 means .

Therefore, we have and .

⇒

Taking square root on both sides, we get

⇒

⇒

⇒ But we know that n < 0, so false.

It should be .

To equal the expression, multiply both sides of the equation by –10n.

⇒   (symbol < changed to > when multiply by minus)

⇒

Hence, the reciprocal of n must be less than –10.

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