Why if $B = \{x : |x+1| ≤ 3 \}$ then $B$ equals $[ -4, \infty )$?

Question

I really don't understand why $B$ is from $-4$ to infinity because

$x+1 ≤ 3$

$x ≤ 2$

and

$-3 ≤ x+1$

$-4 ≤ x$

Shouldn't it be $B = [-4, 2]$?

Answer 1

It is not. $$|x+1|\leq 3 \iff -3 \leq x+1 \leq 3 \iff -4 \leq x \leq 2,$$ so the interval is $[-4,2]$.

Answer 2

for $x\geq -1$ we get $x+1\le3$ this is equivalent to $x\le 2$ or $$x<-1$$ we have $$-x-1\le 3$$ this is equivalent to $$x\geq -4$$ therefore we have $$-4\le x\le 2$$