1. **State the problem:** Solve the inequality $x^2 - 5x + 6 < 0$. 2. **Recall the formula:** For quadratic inequalities, first find the roots of the quadratic equation $x^2 - 5x + 6 = 0$ by factoring or using the quadratic formula. 3. **Factor the quadratic:** $x^2 - 5x + 6 = (x - 2)(x - 3)$. 4. **Find the roots:** Set each factor equal to zero: - $x - 2 = 0 \Rightarrow x = 2$ - $x - 3 = 0 \Rightarrow x = 3$ 5. **Analyze the inequality:** Since the parabola opens upwards (coefficient of $x^2$ is positive), the quadratic is less than zero between the roots. 6. **Write the solution:** $2 < x < 3$. **Final answer:** The solution to $x^2 - 5x + 6 < 0$ is $$2 < x < 3$$.