Simplify

jsasipriya wrote:lx+4l^2>4

Please help me simplify the above.

Thanks

Let me solve it without using any algebra (I'll solve using algebra in another post) :

(You can deduce it in seconds, here I am elaborating a bit just ensure that you learn it using simpler examples)

First lets talk about
|x+4| = 4
This means distance of x from (-4) is 4 in either direction (right,left of a number line)
=> x = -8 and x = 0

Now;
|x+4| > 4
This means distance of x from (-4) is greater than 4 in either direction (right,left of a number line)
=> x < -8 or x > 0

Now the real question :

|x+4|^2 > 4
This means square of distance of x from (-4) is greater than 4 in either direction (right,left of a number line)
=> This means distance of x from (-4) is greater than 2 in either direction (right,left of a number line)
=> x<-6 or x > -2

Hope that helps !

Algebraic approach :

|x+4|^2 > 4

|x+4| = x+4 if (x+4) > 0 and -(x+4) if (x+4) < 0

In either case;
(x+4)^2 > 4
=> x^2+8x+16-4> 0
=> (x+6)(x+2) > 0

=> x < -6 or x > -2