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.

Learn how to solve the inequality 2 - 1/x < 3 with a detailed step-by-step guide. This problem covers key algebraic concepts, including inequality manipulation, the reciprocal rule, and understanding the reversal of inequality signs. Suitable for students in Grades 9-11.

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