# How do you graph and solve #abs(x+1)<=11#?

##### 1 Answer

Solution:

#### Explanation:

Start from a definition of the absolute value.

For non-negative real

For negative real

In short:

if

if

Using this definition, let's divide the domain of the

1.

2.

Case 1. Looking for solutions in interval

Since in this interval

Together with a boundary of the interval, we have come to a solution:

Case 2. Looking for solutions in interval

Since in this interval

Together with a boundary of the interval, we have come to a solution:

So, two intervals are the solution to an original inequality:

These can be combined into

Here is a graph of

graph{|x+1| [-20, 20, -15, 15]}

It illustrates the solution