Question

Solve the following inequality:
$2|x+1|>x-4$

Answer 1

the given equation is

$2|x+1|>x-4$

there are 2 cases

$i.)x<-1,ii.)x>-1$

the respective equations in 2 cases are

$i.\left)2\right(-1-x)>x-4,ii.)2(x+1)>x-4$

in first case

$i.)3x<2$ implies $x<2/3$ and we assumed $x<-1$

therefore the solution is $x<-1$

in second case

$ii.)x>-6$ and we assumed $x>-1$

therefore the solution is

$x>-1$

therefore the overall solution is

$x\in (-\infty ,\infty )$