Question

How do you solve `-2abs(x-3)+6 < -4`?

Answer 1

There are two possibilities: `x-3` (without the absolutes) is positive or negative (the 'switch point is `x=3`)

If it is positive, we can leave out the absolute brackets, is it is negative, we 'turn around' to `-(x-3)=3-x`

(1) `x-3>=0->x>=3`
`-2(x-3)+6<-4->-2x+6+6<-4->`
`-2x<-16->x>8`

(2)`x-3<0->x<3`
`-2(3-x)+6<-4-> -6+2x+6<-4->`
`2x<-4->x<-2`

Conclusion: `x<-2orx>8`