Question: Solve
$x^2 + x - 6 \geq 0$
1. **State the problem:** Solve the inequality $$x^2 + x - 6 \geq 0$$.
2. **Factor the quadratic:**
$$x^2 + x - 6 = (x + 3)(x - 2)$$
3. **Find the roots by setting each factor to zero:**
$$x + 3 = 0 \Rightarrow x = -3$$
$$x - 2 = 0 \Rightarrow x = 2$$
4. **Determine intervals based on roots:**
The critical points divide the number line into three intervals:
$$(-\infty, -3], [-3, 2], [2, \infty)$$
5. **Test each interval:**
- For $$x < -3$$, choose $$x = -4$$:
$$ (x+3)(x-2) = (-4+3)(-4-2) = (-1)(-6) = 6 > 0 $$ (True)
- For $$-3 < x < 2$$, choose $$x = 0$$:
$$ (0+3)(0-2) = 3 \times (-2) = -6 < 0 $$ (False)
- For $$x > 2$$, choose $$x = 3$$:
$$ (3+3)(3-2) = 6 \times 1 = 6 > 0 $$ (True)
6. **Write the solution set:**
$$(-\infty, -3] \cup [2, \infty)$$
**Final answer:**
$$\boxed{x \leq -3 \text{ or } x \geq 2}$$