Solve the given nonlinear inequality. Write the solution set using interval notation. Graph the solution set.$4x^2>9x+9$

Key Concepts: Quadratic Inequalities, Interval Notation, Graphing Solutions Explanation: To solve the inequality, we bring all the terms to one side of the inequality sign so that the other side is equal to zero. And then we use various techniques including factoring, completing the square or using the quadratic formula to solve the inequality. We then represent the solution set as an interval or as a graph or as a combination of both depending on the requirements of the question. Step by Step Solution: Step 1. Write the inequality in standard form by transferring all the terms to the left-hand side to get $4x^2-9x-9>0$ Step 2. Find the critical points of the quadratic by setting the left-hand side equal to zero and solving for $x$. This gives $x=3/4$, $x=-3/2$. These points divide the number line into three intervals. Test each interval (by using a test value in that interval) to see if it satisfies the inequality. The signs of these test expressions determine the solution set. Step 3. The solution set is found to be $(-\infty ,-3/2)\cup (3/4,\infty )$ Final Answer: $(-\infty ,-\frac{3}{2})\cup (\frac{3}{4},\infty )$