sanju09 wrote:For what range of values of 'x' will the inequality 15 x - (2/x) > 1?
A. x > 0.4
B. x < (1/3)
C. (-1/3)< x < 0.4, x >(15/2)
D. (-1/3)< x < 0.4, x >(25)
E. x < (-1/3) and x > (2/5)
Picking numbers shows that E can't be correct.
If we let x = -10, we get:
15(-10) - (2/-10) > 1
-150 + 1/5 > 1
which is clearly not true.
Based on the above, we can also eliminate B.
So, let's look at A, C and D:
A. x > 0.4
C. (-1/3)< x < 0.4, x >(15/2)
D. (-1/3)< x < 0.4, x >(25)
Let's think about 0.4, since that's involved in every choice.
If x = 2/5, then we have:
15(2/5) - 2/(2/5) > 1
6 - 10/2 > 1
6 - 5 > 1
1 > 1
So, if x=2/5, we're right "on the post". Therefore, we need to make x either a tiny bit bigger or smaller.
If we increase the value of x, both terms get bigger; if we decrease the value of x (but keep it positive), both terms get smaller. Therefore, we need a value of x greater than .4.
So, x > .4 needs to be part of our solution.
Only A includes that inequality, therefore A must be correct.
* * *
That said, if -1/3 < x < 0, the inequality will also hold true.
If we let x = -1/3, we get:
15(-1/3) - 2/(-1/3) < 1
-5 + 6 < 1
1 < 1
So -1/3 is also a "post".
If we decrease -1/3, both terms become smaller; if we increase -1/3, but keep it negative, both terms become bigger.
So, if the question wanted the full possible range of values for x, the answer should have been:
F. -1/3 < x < 0 or x > 2/5
