# How to solve 2 absolute value inequalities #abs(x+1)+abs(x-1)<=2#?

##### 1 Answer

With respect to the two absolute value expressions

there are two values of

This gives us three ranges to consider:

(1)

(2)

(3)

**Case 1 :**

Both

so the original inequality can be re-written as

The only value that satisfies

is

**Case 2:**

Of the two terms involving

This is true for all values of

**Case 3:**

Both of the terms involving

**Solution**

Combining all three cases we get

as the solution range.