Question

How do you solve `3(4 - x)(2x + 1)<0`?

Answer 1

x > 4 and x < `-1/2`. In other words, x is outside `[ -1/2, 4 ]`

Explanation:

Drop the positive factor 3.
`-2 x^2 + 7 x +4 < 0`.
`( x - 7/4 )^2 > 81/16`
`| x - 7/4 | > 9/4`.
If `| x - a | > b, x > a + b and x < a - b`
Here, `x > 4 and x < -1/2`.