Question

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

Answer 1

The answer is `x in ]-1/2, 4[`

Explanation:

Let `f(x)=3(4-x)(2x+1)`

We build a sign chart

`color(white)(aaaa)` `x` `color(white)(aaaaaa)` `-oo` `color(white)(aaaa)` `-1/2` `color(white)(aaaa)` `4` `color(white)(aaaaa)` `+oo`

`color(white)(aaaa)` `2x+1` `color(white)(aaaaaaa)` `-` `color(white)(aaaa)` `+` `color(white)(aaaa)` `+`

`color(white)(aaaa)` `4-x` `color(white)(aaaaaaaa)` `+` `color(white)(aaaa)` `+` `color(white)(aaaa)` `-`

`color(white)(aaaa)` `f(x)` `color(white)(aaaaaaaaa)` `-` `color(white)(aaaa)` `+` `color(white)(aaaa)` `-`

Therefore,

`f(x)>0` when `x in ]-1/2, 4[`