# How do you solve 3 > abs(a + 1)?

Jun 2, 2015

$\left\mid a + 1 \right\mid$ is either equal to $a + 1$ ( if $a + 1 > 0$ )
or $- a - 1$ ( if $a + 1 < 0$ )

Thus :

• $3 > a + 1$
$3 - 1 > a$ ( we substract 1 on each side )
$2 > a$
$a < 2$

Or :

• $3 > - a - 1$
$3 + 1 > - a$ ( we add 1 on each side )
$4 > - a$
$- 4 < a$ ( we multiply by $- 1$ on each side, and thus $>$ becomes $<$ )
$a > - 4$