The Math practice question for the day is an inequality question. Inequality is one of the easiest set of questions if the basic concepts are well understood.
Question
For what range of values of 'x' will the inequality 15x -
> 1?
A. x > 0.4
B. x <
C. -
< x < 0.4, x >
D. -
< x < 0, x >
E. x < -
and x >
The correct choice is (D) and the correct answer is
- < x < 0, x > .
Explanatory Answer
We can rewrite the above inequality as 15x -
- 1 > 0
i.e.,
> 0
or
> 0.
Factorizing we get,
> 0
The above inequality will hold good if the numerator and denominator are both positive or are both negative.
Case 1: When (5x - 2)(3x + 1) > 0 and x > 0
This will hold true for values of 'x' that do not lie between
and
and for x > 0.
Combining all these conditions, we get x >
Case 2: When (5x - 2)(3x + 1) < 0 and x < 0
This will hold true for the following values of 'x':
< x <
and x < 0.
Combining, we get
< x < 0.
Therefore, the final range for which the above inequality will hold true is given by
< x < 0 and
x >
.
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