inequality

What values of x satisfy |x - 4| + |x + 4| <= 20?

 

x-4 is positive  when x>4

x+4 is positive when x>-4

 

So we have three regions to consider.

x<=-4,    x>=4    and  -4

 

If x <= -4 then

|x - 4| + |x + 4| <= 20

 -(x-4) +  -(x+4) <=20

-x+4 -x-4  <= 20

-2x<= 20

x>=-10

So the statement is true for   -10 <=x <= -4

 

You can do the other 2 regions.