In this lesson, students solve absolute value inequalities by reasoning about distances on a number line. They begin by examining a context in which there is a manufacturing tolerance. Students write values that fall within that tolerance and draw the range of solutions on a number line. Then, they write an inequality to represent the distance from the target value. In the following activity, students solve absolute value inequalities and draw the solution on a number line using reasoning about distance from a number.

In these materials, there is no emphasis on using “and” and “or” in a precise way. Instead, students are asked to draw their solutions on a number line. This helps students focus on understanding the meaning of their solutions.