Inequalities are one of the foundational subjects in high school math curricula, but there is a lack of academic research into how students learn certain types of inequalities. This article fills part of the research gap by presenting the findings of a study that examined high school students' methods of approaching absolute value inequalities, their common mistakes, misconceptions, and the possible sources of these mistakes and misconceptions. The research study used two tools--a questionnaire and personal interviews. The questionnaire was given to 481 students in the 10th and 11th grades in Israel who studied mathematics at intermediate and advanced levels. It was administered after the students had studied inequalities. Thirty-two students were interviewed in order to find their ways of thinking and the sources of their errors. The main types of mistakes that students consistently made when solving absolute value inequalities were found. Based on the study's findings, teachers can understand students' thought processes and use this understanding to conduct remediation and enhance mathematics instruction.