Solve the following inequality.

The solution set is
(Type your answer in interval notation. Use integers or fractions for any numbers in the expression. Type an exact answer, using radicals as needed.)

To solve the inequality , first, we rearrange it to one side:

Next, we can factor the polynomial if possible. We can test for rational roots using the Rational Root Theorem. After testing , we find it is a root. We perform synthetic division or polynomial long division to factor it:

Next, we can apply the same methods of factorization or the Rational Root Theorem to the quartic, but let’s proceed with finding roots via numerical or graphical methods, or methods like Descartes’ rule of signs.

After determining the roots of the quartic polynomial, we can find intervals for testing the inequality. Including in our calculations offers us simplified evaluations in intervals around the roots.

After testing intervals defined by the roots, we can conclude that:

The solution set is .