How do you solve #abs(5 - 1/x)< 2#?
First interpret the modulus to get:
Then apply arithmetic operations to arrive at:
Next multiply all parts by
Since this forces
Multiply all parts by
Dividing the first of these by
Diving the second by
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 (