i get the basic abs value inequalities e.g. abs(1+x)>3 etc...

 

how do we solve in general for abs valued inequalities like this?? abs(x+1)+abs(x+3)+5>abs(4+x) etc....

 

im alittle confused.

 

thanks in advance.

You need to set up a number line and transform the equation in such a way that the right side is equal to 0. Look for values for x where this is true, and then check if you increase or decrease x to let the equation equal > 0.

i get the basic abs value inequalities e.g. abs(1+x)>3 etc...

 

how do we solve in general for abs valued inequalities like this?? abs(x+1)+abs(x+3)+5>abs(4+x) etc....

 

im alittle confused.

 

thanks in advance.

For each abs term, divide the x axis into 2 parts depending on whether the argument is + or -. For example, abs(x+1) divide at x = -1. Then for each part you have either x+1 (x > -1) or -(x+1) (x < -1), without abs.

 

Then analyze the expression for each part. In your example, you may need several pieces, but for each piece it should be easy enough.