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If \(\frac{0.0019}{-x} > 2\), then which of the following could be the value of \(x\) ?
A. \(-10^{-1}\)
B. \(-10^{-2}\)
C. \(-10^{-3}\)
D. \(-10^{-4}\)
E. \(10^4\)
A. \(-10^{-1}\)
B. \(-10^{-2}\)
C. \(-10^{-3}\)
D. \(-10^{-4}\)
E. \(10^4\)
30 Nov 2021, 07:07
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Official Solution:
If \(\frac{0.0019}{-x} > 2\), then which of the following could be the value of \(x\) ?
A. \(-10^{-1}\)
B. \(-10^{-2}\)
C. \(-10^{-3}\)
D. \(-10^{-4}\)
E. \(10^4\)
First of all, notice that \(-10^{-1} < -10^{-2} < -10^{-3} < -10^{-4} < 10^4\)
Also, notice that since \(\frac{0.0019}{-x}\) is positive, then \(x\) must be a negative number. We can rule out option E.
Multiply \(\frac{0.0019}{-x} > 2\) by \(x\) and flip the sign because we are multiplying by a negative number: \(-0.0019 < 2x\);
\(x > -0.00095\);
\(x > (-10^{-3})*0.95\)
Since \((-10^{-3})*0.95 > -10^{-3}\), then \(x>(-10^{-3})*0.95 > -10^{-3}\).
\(x\) can only be \(-10^{-4}\) from the options.
Answer: D
If \(\frac{0.0019}{-x} > 2\), then which of the following could be the value of \(x\) ?
A. \(-10^{-1}\)
B. \(-10^{-2}\)
C. \(-10^{-3}\)
D. \(-10^{-4}\)
E. \(10^4\)
First of all, notice that \(-10^{-1} < -10^{-2} < -10^{-3} < -10^{-4} < 10^4\)
Also, notice that since \(\frac{0.0019}{-x}\) is positive, then \(x\) must be a negative number. We can rule out option E.
Multiply \(\frac{0.0019}{-x} > 2\) by \(x\) and flip the sign because we are multiplying by a negative number: \(-0.0019 < 2x\);
\(x > -0.00095\);
\(x > (-10^{-3})*0.95\)
Since \((-10^{-3})*0.95 > -10^{-3}\), then \(x>(-10^{-3})*0.95 > -10^{-3}\).
\(x\) can only be \(-10^{-4}\) from the options.
Answer: D
