Question 1019710
i believe the answer is going to be x < -k and x > k


here's how to figure.


start with abs(x) > k


abs(x) means the same as |x| which means absolute value of x.


so start with abs(x) > k.


now abs(x) is equal to x if x > 0 and abs (x) is equal to -x if x < 0.


therefore:


abs(x) > k can be broken up into two equations, one where x is greater than 0 and one where x is smaller than 0.


you get:


-x > k when x is smaller than 0, and x > k when x is greater than 0.


when x is smaller than 0, the equation of -x > k is solved for x as follows:


start with -x > k
multiply both sides of this equation by -1 to get x < -k.
when you multiply both sides of an inequality by a negative number, the inequality reverses.
so, when x < 0, you get x < -k.


when x is greater than 0, the equation of x > k is solved for x as follows:


start with x > k
you're done since the equation has already been solved.


so you have x < -k or x > k.


in interval notation, this solution would be shown as (-infinity,-k) union (k,infinity).


if you were able to graph this inequality, you would get a graph that looks like this:


<img src = "http://theo.x10hosting.com/2016/021404.jpg" alt="$$$" </>