# How do you solve and write the following in interval notation: #1/|x+5| >2#?

##### 1 Answer

#### Explanation:

First of all, we have to exclude the value when the inequality is undefined because the denominator is zero:

In all cases, except this,

Both sides of an inequality can be multiplied by a POSITIVE number, leaving the sign of inequality as is.

Since

or

Next transformation is division of both sides of inequality by POSITIVE number

Recall the definition of

Consider now two cases (we excluded

Case 1.

Then

or, subtracting

We have to combine this with an inequality that defines our case,

Both inequalities result in'

Case 2.

Then

or, add

or, subtracting

We have to combine this with an inequality that defines our case,

Both inequalities result in'

Final solution is

Here is an illustrative graph of a function

graph{1/|x+5|-2 [-10, 2, -5, 5]}