There are basically three cases or situations that can arise when working with them. By guessing and checking we can answer the following three questions.
Case 1: | X | = n can be solved using X = -n or X = n.
Case 2: | X | < n can be solved using -n < X < n.
Case 3: | X | > n can be solved using X < -n or X > n.
Use the following steps to solve an absolute value equation or inequality.
Step 1: Isolate the absolute value.
Step 2: Identify the case and apply the appropriate theorem.
Step 3: Solve the resulting equation or inequality.
Step 4: Graph the solution set and express it in interval notation.
Instructional Video: Absolute Value Inequalities