inequality 
3
x
2
−
4
x
−
4
>
0
3x 
2
 −4x−4>0, graph the solution

Here is the graph of the inequality \(3x^2 - 4x - 4 > 0\). The solution regions are shaded in green:

- The left region corresponds to \(x < -\frac{2}{3}\).
- The right region corresponds to \(x > 2\).

The open circles at \(x = -\frac{2}{3}\) and \(x = 2\) indicate that these points are not included in the solution set.

Would you like more details or have any questions?

Here are some related questions:
1. What is the significance of the discriminant in a quadratic equation?
2. How does the sign of the leading coefficient affect the direction of the parabola?
3. Can you solve a similar inequality but with a different quadratic expression?
4. What are the steps to solve a quadratic inequality involving "less than or equal to"?
5. How can quadratic inequalities be applied in real-world scenarios?

**Tip:** Always check the intervals between the roots to determine where the inequality holds true.

Explore how to graph the quadratic inequality 3x^2 - 4x - 4 > 0 with detailed solutions and graphical representation. This problem involves understanding quadratic inequalities and graphing techniques, suitable for advanced high school students.

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