Question

( 4x -1 ) ^ -1 > 0

Answer 1

\[\dfrac{1}{4x - 1} > 0\]Notice carefully:

When the denominator is positive, the inequality always holds, since a positive number divided by a positive number will ALWALS be greater than zero no matter how small it is.

The only place where the inequality will not hold is where the denominator itself is negative. That would make the whole fraction negative and the inequality will obviously not hold.

You're never supposed to include excluded values in your answer (obviously!). So keep in mind that you are not supposed to include the value of \(x\) for which the denominator becomes equal to zero.

Answer 2

"ALWALS" lol

Answer 3

To sum it all up,

When the denominator is greater than zero, i.e., \(4x - 1 > 0\), the inequality will hold.

- - -

You don't really need the other two cases in this question, but I'll write them down...

When the denominator is less than zero, i.e., \(4 x - 1 < 0\), the inequality will not hold.

When the denominator is zero, i.e., \(4x - 1 = 0\), the fraction is not defined.

Answer 4

so what is the working for this question ?

Answer 5

is that all ?

Answer 6

To solve the inequality, you need to find out all the \(x\)-values that make the inequality hold true.

For instance,

\(x + 1 > 0\) holds true for all \(x> -1\).

Similarly, here, as I said, this inequality you have when \(4x - 1\) is positive. This would mean that \(4x - 1>0.\) You have to find out the \(x\) for which it is true, so you will have to solve this inequality.

Answer 7

thank you