Question

Solve the following systems of inequality:

$|x^2+5x|<6,|x+1|<2$

Answer 1

1. $\mid x^2+5x\mid <6$

$\Rightarrow -6<x^2+5x<6$

a. $0<x^2+5x+6$

$\Rightarrow (x+3)(x+2)>0$

$\Rightarrow x\in (-\infty ,2)$ & $(3,\infty )$ - Equation a

b. $x^2+5x-6<0$

$\Rightarrow (x+6)(x-1)<0$

$\Rightarrow x\in (-6,1)$ - Equation b

For 1, intersection of a & b are taken $\Rightarrow x\in (-6,1)$ - Equation 1

2. $\mid x+1\mid <2$

$\Rightarrow -2<x+1<2$

$\Rightarrow -3<x<1$

$\Rightarrow x\in (-3,1)$ - Equation 2

Now, for solution to Equation 2 & Equation 1 simultaneously, intersection of 1& 2 ,

$\Rightarrow x\in (-3,1)$