To solve the inequality:

$2 - \frac{1}{x} < 3$

we can isolate $x$ by following these steps:

1. Subtract 2 from both sides:

   $-\frac{1}{x} < 1$

2. Multiply both sides by -1 (remember, when multiplying or dividing by a negative number, the inequality sign reverses):

   $\frac{1}{x} > -1$

3. Take the reciprocal of both sides (again, the inequality sign reverses when we take reciprocals if they are both positive or both negative):

   $x > -1$

Solution:

The solution to the inequality is: $x > -1$

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Would you like more details, or do you have questions?

Here are related questions that may expand your understanding:

1. What happens if we add more terms to the inequality, like $2 - \frac{1}{x} + 3x < 3$?
2. How do we solve similar inequalities with quadratic terms, like $2 - \frac{1}{x^2} < 3$?
3. What are the steps for solving inequalities with absolute values, such as $2 - \left|\frac{1}{x}\right| < 3$?
4. How can we interpret the inequality solution on a number line?
5. What would the solution be if we had $2 - \frac{1}{x} > 3$ instead?

Tip: Always remember to reverse the inequality sign when multiplying or dividing both sides by a negative.