Math Help - help

1. help

||x - 4|- 3| + 4 < |2x + 5|

2. Originally Posted by Freaky-Person
||x - 4|- 3| + 4 < |2x + 5|
$||x-4|-3|+4<|2x+5|$
Again, you need to consider to cases for absolute for one non-negative and one negative. That is the standard way of doing these nasty ones.

$2x+5\geq 0$
$x\geq -2.5$ for non-negative value.
$x<-2.5$ for negative value.

$|x-4|-3\geq 0$
$|x-4|\geq 3$
$x-4\geq 3 \mbox { or }x-4\leq -3$
$x\geq 7 \mbox{ or }x\leq 1$ for non-negative value.

$|x-4|-3<0$
$|x-4|<3$
$-3
$1
For negative value.

Now we divide the problem into cases,
$x<-2.5$ thus, $2x+5<0, |x-4|-3>0$
$-2.5\leq x\leq 1$ thus, $2x+5,|x-4|-3>0$
$1 thus, $2x+5>0, |x-4|-3<0$
$7\leq x$ thus. $2x+5>0, |x-4|-3>0$.

And you do what I did before.
In each of these cases the absolute sign disappearsn and you deal with a different inequality. If the set of $x$ contradicts the condition from the intersection.