Question

How do you solve `5x ^ { 2} - 9x < - 4`?

Answer 1

`4/5 lt x lt 1`

Explanation:

We have,

`color(white)(xxx)5x^2 -9x lt -4`

`rArr 5x^2 -9x +4 lt 0` [Transpose `-4` to L.H.S.]

`rArr 5x^2 -5x -4x + 4 lt 0` [Break `-9x` as `-5x -4x`]

`rArr 5x(x - 1) - 4(x - 1) lt 0` [Group the like terms]

`rArr (x -1) (5x -4) lt 0` [Group again]

Now for the inequality to be true,

Either `(x - 1) lt 0` or `(5x - 4 ) lt 0`

So, Either `x lt 1` or `x lt 4/5`

If `x lt 4/5`, then it is automatically `lt 1`. Then, Both Term will be negative. So, It can't be possible.

So, The interval of values for `x` is :- `4/5 lt x lt 1`

Hence Explained.