Why is it |x∣ ≤ 2 means x ≤ 2 and x ≥ −2
or −2 ≤ x ≤ 2

Question

Why is it |x∣ ≤ 2 means x ≤ 2 and x ≥ −2 
or −2 ≤ x ≤ 2

anonymous · Answer

Either or, but the second one is the combined answer. It means this because of the absolute value bars. The absolute value turns what's inside positive, even if it's a negative value.

moongazer · Answer

could you explain further?

anonymous · Answer

It's kind of hard to go farther since that's all there is to it. You can plug in any negative number in for x and it will turn into the positive value of that number. However, the definition of absolute value is thge distance of the number to zero.

zarkon · Answer

$|x|$ is the distance to the origin 

if you want $|x|\le 2$ then you want all the points that are within 2 units from the origin

anonymous · Answer

is zarkon's answer not sufficient? |dw:1339119863980:dw|

mertsj · Answer

|x| < 2 means that the numbers are less than 2 units from 0.  Clearly, as Satellite and Zarkon have explained, those numbers have to be between -2 and 2

moongazer · Answer

ok I get it now thanks :)