The National Council of Teachers of Mathematics [NCTM] noted that middle and high school students are expected to be able to both explain inequalities by using mathematical symbols and understand meanings by interpreting the solutions of inequalities. Unfortunately, research has revealed that not only do middle and high school students hold misconceptions and have difficulties with inequalities, but college students also possess some of these same misconceptions, thus demonstrating difficulties in solving and interpreting inequalities. This research specifically focused on mathematics pre-service teachers' understandings of linear and quadratic inequalities to determine whether they possess common misconceptions and difficulties with inequalities. Results provided evidence that many pre-service teachers have misconceptions (only one value makes inequality correct, and treating inequality's solution as the same way treating equality's solution) and difficulties (e.g., lack of understanding what inequalities' questions ask to find, having trouble with representing inequalities' solutions, and arithmetic errors) that cause them to misunderstand inequalities.