Question

How do you solve `-2x^2+10<8x` using a sign chart?

Answer 1

The solution are `x<-5` and `x>1`

Explanation:

Let's rewrite the expression
`f(x)=2x^2+8x-10>0`
so factorising
`(2x-2)(x+5)=2(x-1)(x+5)>0`
So the values of x to be taken in consideration are `x=1` and `x=-5`

Let 's do the sign chart
`x` `color(white)(aaa)` `-oo` `color(white)(aaaa)` `-5` `color(white)(aaaa)` `1` `color(white)(aaaa)` `+oo`
`x-1` `color(white)(aaaa)` `-` `color(white)(aaaa)` `-` `color(white)(aaaa)` `+`
`x+5` `color(white)(aaaa)` `-` `color(white)(aaaa)` `+` `color(white)(aaaa)` `+`
`f(x)` `color(white)(aaaaa)` `+` `color(white)(aaaa)` `-` `color(white)(aaaa)` `+`

So the values of x are `x<-5` and `x>1`