How do you graph #abs(x+y)1#?

Question

How do you graph #abs(x+y)>1#?

Eva Adamson · Accepted Answer

There's plenty of ways one could do this, but let's just start by thinking about what this could look like.  We will think about the boundary of this region: #|x+y| = 1#.  Here we think about the two cases of absolute value: positive and negative.  If #x+y>0#, the boundary is simple: 
#|x+y| = x+y = 1 implies y = -x + 1 #
which is just a line going down from (0,1) to (1,0).  If #x+y<0#, the boundary is another line:
#|x+y| = -(x+y) = 1 implies y = -x - 1 #
which is a line going from (-1,0) to (0, -1).  Therefore, there are three regions: 
- Below the left line
- Between the lines
- Above the right line It is clear that the more outside of those you get, the more #>1# you'll get, hence it is the regions outside the strip that are included.  In case my description wasn't sufficient, here's the plot:
 graph{|x+y|=1 [-10, 10, -5, 5]}

Hazel Anglin · Answer

undefined To graph the inequality abs(x+y) > 1, you first rewrite it as two separate inequalities: x+y > 1 and x+y < -1. Then, you graph the lines x+y = 1 and x+y = -1 (dashed lines since the inequalities are strict). Finally, you shade the regions above the line x+y = 1 and below the line x+y = -1 to represent the solution to the original inequality abs(x+y) > 1.

How do you graph #abs(x+y)&gt;1#?

How do you graph #abs(x+y)>1#?