Okay, so here's the problem. $$|x^2+x-6|\ge|2x-4|+4$$ What I've done is divided that problem into 4 different options.
a) When the right absolute value and the left one are positive
b) right is positive, left is negative
c) right is negative, left is positive
d) both are negative
I then drew all the x values on a number line, and just looked at the edges, with both satisfy my absolute value.
Therefore, the answer is $(-\infty,-5.531] \cup[3, \infty)$
Both of those numbers are part of my number line and they both satisfy the whole absolute value...
Here is my paper:
