Quadratic Inequality

Explanation

We will solve the inequality:

Factor the quadratic equation:

The zeros (roots) of the equation are:

We test points on the number line:

• For $x < -3$ (e.g., $-4$): $(-4-2)(-4+3) = (-6)(-1) = 6$ (Positive)
• For $-3 < x < 2$ (e.g., $0$): $(0-2)(0+3) = (-2)(3) = -6$ (Negative)
• For $x > 2$ (e.g., $3$): $(3-2)(3+3) = (1)(6) = 6$ (Positive)

Since the inequality sign is $> 0$ (positive), the solution region is:

Based on the given statements:

1. $x > 2$ (Matches)
2. $-3 < x < 2$ (Does not match)
3. $x < -3$ (Matches)
4. $x > -3$ (Does not match)

Thus, the inequality is satisfied by statements $1$ and $3$.