Questions: Solve the inequality. Write the solution set in interval notation if possible. Simplify your answer, if necessary. 3 d^3+5 d^2<3 d+5 The solution set is.

Solution Steps

We start with the inequality \(3d^3 + 5d^2 < 3d + 5\). Rearranging this gives us the polynomial inequality \(3d^3 + 5d^2 - 3d - 5 < 0\).

Next, we find the roots of the polynomial equation \(3d^3 + 5d^2 - 3d - 5 = 0\). The roots will help us identify the critical points that divide the number line into intervals.

The roots of the polynomial are approximately \(d = -\frac{5}{3}\) and \(d = -1\). We test the intervals \((- \infty, -\frac{5}{3})\) and \((-1, 1)\) to determine where the inequality \(3d^3 + 5d^2 - 3d - 5 < 0\) holds true.

The solution set, where the inequality is satisfied, is expressed in interval notation as \( (-\infty, -\frac{5}{3}) \cup (-1, 1) \).

Final Answer