# Math Help - modulus equation

1. ## modulus equation

am trying to solve for x in this equation

$x^2-\mid x \mid - 12 < 0$
$\mid x \mid <12-x^2$
$\mid x \mid^2 >{(12-x^2})^2$ squaring both sides

i end up with $x^4 - 24x^2+144=0$ can i get some helf solving for x. that if what i did was correct.

2. Hi

I suggest you to separate the 2 cases $x\leq 0$ and $x \geq 0$

In the first case you get $x^2 + x - 12 < 0$

$(x+4)(x-3) < 0$

Find the solutions and take the ones that are $\leq 0$

Do the same for the second case and finally join the 2 sets of solutions

3. Originally Posted by sigma1
am trying to solve for x in this equation

$x^2-\mid x \mid - 12 < 0$
$\mid x \mid <12-x^2$
$\mid x \mid^2 >{(12-x^2})^2$ squaring both sides

i end up with $x^4 - 24x^2+144=0$ can i get some helf solving for x. that if what i did was correct.
Hi sigma1,

you need c-ordination here,

you have made errors with polarity above.

$x^2-|x|-12<0$

If x is positive, this is

$x^2-x-12<0$

$(x-4)(x+3)<0$

this is negative if one factor is positive and the other negative.
If -3<x<4 the left factor is negative and the right one positive.
But remember, x must be positive here.
If x>4, they are both positive.
If x<-3 they are both negative.

If x is negative, this is

$x^2+x-12<0$

$(x-3)(x+4)<0$

This can be evaluated in the same way as above.