Question

`| {x}^(2) + 3x +2 | < 2x + 4`
solve the following inequalities​

Answer 1

`\\ \tt\hookrightarrow |x^2+3x+2|<2x+4`

Either

`\\ \tt\hookrightarrow x^2+3x+2<-2x-4`

`\\ \tt\hookrightarrow x^2+3x+2x<-4-2`

`\\ \tt\hookrightarrow x^2+5x+6<0`

`\\ \tt\hookrightarrow (x+2)(x+3)<0`

`\\ \tt\hookrightarrow x<-2\:or \:x\:-3`

Or

`\\ \tt\hookrightarrow x^2+3x+2<2x+4`

`\\ \tt\hookrightarrow x^2+x-2<0`

`\\ \tt\hookrightarrow x^2+2x-x-2<0`

`\\ \tt\hookrightarrow (x+2)(x-1)<0`

`\\ \tt\hookrightarrow x<-2\:or \:x<1`

So

`\\ \tt\hookrightarrow x\in (-3,1)`