Inequality

[DCJ]

Double-checking since I saw what seems to be a mistake in a text

(-1/x)>17

Does the above equation simplify to
x<(-1/17) or x>(-1/17)

[ankitns]

X < -1/17

Cheers.

[gmat_2010]

It will be X > -17

The inequality sign changes twice. Once for inversion of 1/x to x. One for changing -X to X. Hence, the sign remains the same in the final answer.

(-1/x)>17
Therefore, -x < 1/17
Therefore, x > -1/17

Check:
Assume x = -1/18 which is greater than -1/17

(-1/x) = 18 which is greater than 17.

[DCJ]

X < -1/17 is the correct answer. -1/18<-1/17

[Ian Stewart]

X < -1/17 is the correct answer. -1/18<-1/17

-1/18 is greater than -1/17, since it is closer to zero on the number line.

In this inequality:

-1/x > 17

x must be negative, since the value of -1/x is positive (it's greater than 17). So when we multiply by x on both sides, we're multiplying by a negative, and we need to reverse the inequality:

-1/x > 17
-1 < 17x
-1/17 < x

and since we know x is negative, we know that -1/17 < x < 0.

[srisanj4]

Agreed. x>-1/17