In this lesson, the speaker discusses solving inequalities by using compound inequalities, emphasizing the importance of finding values that satisfy both conditions. The example given involves finding the values of ‘x’ in two inequalities, demonstrating how to graph these on a number line. The lesson highlights the steps necessary to isolate ‘x’ while ensuring that both inequalities hold true. Finally, it underscores the importance of understanding the relationships between the values involved in compound inequalities.