# How do you solve the inequality #2<=abs(4-x)<7# and write your answer in interval notation?

##### 1 Answer

#### Explanation:

First, recall the rules of absolute values in inequality expressions.

**Absolute value is less than something rule**

If

**Absolute value is greater than something rule**

If

The inequality we are given can be broken into two parts.

**First part: Less than rule**

Applying the "less than rule" gives

Subtract

Divide by

**Second part: Greater than rule**

Applying the "greater than rule" gives

Either

Solving both for

Either

**Finally, combine all solutions into one**

The solution:

The solution: Either

ANSWER:

Here is what the graph would look like: