# Math Help - Solving Absolute value quadratic inequalities

1. ## Solving Absolute value quadratic inequalities

Solve | x2 - 4| < 8
I have not done any absolute value quadratic inequalities, here is my attempt. Please check my work, thank you!

|x2 - 4| < 8
|x2| +4 < 8
|x2| - 4 < 0
(|x2| -2 ) ( |x2| + 2) < 0

Do we stop here? What do we do next?
So, a. -x2 - 2 < 0 and b. x2 -2 < 0 & c. - x2 +2 < 0 and d. x2 + 2 < 0

2. ## Re: Solving Absolute value quadratic inequalities

Originally Posted by sakonpure6
Solve | x2 - 4| < 8
I have not done any absolute value quadratic inequalities, here is my attempt. Please check my work, thank you!
None of that is correct.
$\\|x^2-4|<8\\-8

Have a look at this

3. ## Re: Solving Absolute value quadratic inequalities

how would you solve |x^2 - 4| > 8 ?

4. ## Re: Solving Absolute value quadratic inequalities

Originally Posted by sakonpure6
how would you solve |x^2 - 4| > 8 ?
Can you solve $x^2>12\text{ or }x^2<-4~?$

5. ## Re: Solving Absolute value quadratic inequalities

Originally Posted by sakonpure6
how would you solve |x^2 - 4| > 8 ?
Copy what Plato did, but change the $<$ sign to a $>$ sign.

$|x^2-4|>8$

$(x^2-4)<-8$ or $8<(x^2-4)$

$x^2<-4$ or $12 < x^2$

There are no real values of $x$ with $x^2<-4$, so
$x< -\sqrt{12}$ or $\sqrt{12}< x$.

6. ## Re: Solving Absolute value quadratic inequalities

Oh okay thank you guys!