1. **Stating the problem:** We need to understand and solve inequalities, which are mathematical expressions involving \(<\), \(>\), \(\leq\), or \(\geq\).\n\n2. **Formula and rules:** Inequalities are solved similarly to equations, but when multiplying or dividing both sides by a negative number, the inequality sign reverses.\n\n3. **Example:** Solve \(3x - 5 > 7\).\n\n4. **Step 1:** Add 5 to both sides: \(3x - 5 + 5 > 7 + 5\) which simplifies to \(3x > 12\).\n\n5. **Step 2:** Divide both sides by 3: \(\frac{3x}{3} > \frac{12}{3}\). Show cancellation: \(\frac{\cancel{3}x}{\cancel{3}} > \frac{12}{3}\) so \(x > 4\).\n\n6. **Interpretation:** The solution means all values of \(x\) greater than 4 satisfy the inequality.\n\n7. **Important:** If dividing by a negative number, reverse the inequality sign. For example, if \(-2x < 6\), dividing by \(-2\) gives \(x > -3\).\n\nThis is the basic approach to solving inequalities.