# How do you solve #abs(5 - 1/x)< 2#?

##### 1 Answer

First interpret the modulus to get:

Then apply arithmetic operations to arrive at:

#### Explanation:

Next subtract

Next multiply all parts by

Since this forces

Multiply all parts by

Dividing the first of these by

Diving the second by

So

In general, you can apply the following operations to an inequality and preserve its truth:

(1) Add or subtract the same value from all parts of the inequality.

(2) Multiply or divide all parts by the the same positive value.

(3) Multiply or divide all parts by the same negative value and reverse the inequalities (