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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step-by-step explanation:

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is