If 0.0019/-x > 2, then which of the following could be the value of x?

\(\frac{0.0019}{-x} > 2\)

i.e. \(\frac{-0.0019}{2} < x\)

i.e. \(x > -0.00095\)

i.e. \(x > -0.95*10^{-3}\) Also x must be negative

Answer: Option D...

\(\frac{0.0019}{-x} > 2\)

~ \(\frac{0.0020}{-2} > x\)

= \(-0.0010 > x\)

= \(-\frac{1}{10000} > x\)

= \(\frac{-1}{10^4} > x\)

= \(-10^{-4} > x\), Answer must be (D)

Rule of (-)Negative Integer Exponents: Take the Reciprocal of the Base and change the Integer Exponent to a (+)Pos. Sign


(1st Inference)

since the NUM has a (+)Pos. Value, we need the SAME Sign in the DEN in order to have the Left Hand Side be greater than > (+)Pos. 2

The DEN = -X

therefore, we need a -Neg. Value for X such that when we plug-it in to -(X) we will have a 'Double-Negative' and the DEN will be (+)positive

Eliminates Answer -E-


(2nd) Looking at the Remaining Answer Choices, they are all Powers of 10 with (-)Negative Integer Exponents. When we take the Reciprocal of the Base, the 10 will move from the DEN to the NUM and the Exponent will become (+)Positive.

(.0019) / - (-10^ -n) > 2

(.0019) / 10^ -n > 2

(.0019) * (10)^ +n > 2

at MINIMUM, we will need the Integer Exponent to equal 4 in order to move the Decimal Point 4 Places to the Right.

0.019 < 2
00.19 < 2
001.9 < 2
0019 -----> 19 > 2

D is the Correct Answer

-(10 ^ -4th Power)