# How do you solve #abs(x+1)+ abs(x-1)<=2#?

##### 1 Answer

With moduli it is useful to split into cases at the point that the sign of the enclosed expression changes.

Case (a) :

Dividing both ends by **reversing the inequality** we get:

Notice that we have to reverse the inequality, because we are dividing by a negative number.

So in Case (a) we have

These conditions cannot be satisfied at the same time, so Case (a) yields no solutions.

Case (b) :

So the target inequality is satisfied for all

That is

Case (c) :

So in Case (c) the inequality is never satisfied.

So the solution is