mostafaehabaly
Answered

Welcome to Westonci.ca, where your questions are met with accurate answers from a community of experts and enthusiasts. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.


[tex] | {x}^{2} + 3x +2 | < 2x + 4[/tex]
solve the following inequalities​

Sagot :

[tex]\\ \tt\hookrightarrow |x^2+3x+2|<2x+4[/tex]

Either

[tex]\\ \tt\hookrightarrow x^2+3x+2<-2x-4[/tex]

[tex]\\ \tt\hookrightarrow x^2+3x+2x<-4-2[/tex]

[tex]\\ \tt\hookrightarrow x^2+5x+6<0[/tex]

[tex]\\ \tt\hookrightarrow (x+2)(x+3)<0[/tex]

[tex]\\ \tt\hookrightarrow x<-2\:or \:x\:-3[/tex]

Or

[tex]\\ \tt\hookrightarrow x^2+3x+2<2x+4[/tex]

[tex]\\ \tt\hookrightarrow x^2+x-2<0[/tex]

[tex]\\ \tt\hookrightarrow x^2+2x-x-2<0[/tex]

[tex]\\ \tt\hookrightarrow (x+2)(x-1)<0[/tex]

[tex]\\ \tt\hookrightarrow x<-2\:or \:x<1[/tex]

So

[tex]\\ \tt\hookrightarrow x\in (-3,1)[/tex]

Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.