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Name: ___________________________________ Algebra II Investigating Compound Inequalities Group 1 |x| ≤ 3 and |x| < 3 1. Evaluate |x| ≤ 3 for x = {–5, –4, –3, –2, –1, 0, 1, 2, 3, 4, 5}. Determine which integers satisfy the inequality. Graph the solution set on the number line. 2. Now determine which real numbers satisfy the inequality |x| ≤ 3 and graph the solution on the number line. 3. Write a compound inequality representing the second graph. Does it represent an inequality that uses the word OR or the word AND? 4. Now graph |x| < 3 on a number line and write a corresponding compound inequality. What changes between the graph in step 2 and the compound inequality in step 3? 5. Using the word “distance,” explain the meaning of the graph in step 2. Then explain the meaning of the graph in step 4. 6. If you had a simple absolute value equation |x| = 3, you would write two equations: x = 3 (positive equation) x = –3 (negative equation) Try to write two equations for |x| < 3. Compare your solutions to your compound inequality from step 4? Do you notice anything? Name: ___________________________________ Algebra II Investigating Compound Inequalities Group 2 |x| ≥ 3 and |x| > 3 1. Evaluate |x| ≥ 3 for x = {–5, –4, –3, –2, –1, 0, 1, 2, 3, 4, 5}. Determine which integers satisfy the inequality. Graph the solution set on the number line. 2. Now determine which real numbers satisfy the inequality |x| ≥ 3 and graph the solution on the number line. 3. Write a compound inequality representing the second graph. Does it represent an inequality that uses the word OR or the word AND? 4. Now graph |x| > 3 on a number line and write a corresponding compound inequality. What changes between the graph in step 2 and the compound inequality in step 3? 5. Using the word “distance,” explain the meaning of the graph in step 2. Then explain the meaning of the graph in step 4. 6. If you had a simple absolute value equation |x| = 3, you would write two equations: x = 3 (positive equation) x = –3 (negative equation) Try to write two equations for |x| > 3. Compare your solutions to your compound inequality from step 4? Do you notice anything? Name: ___________________________________ Algebra II Investigating Compound Inequalities Group 3 |x – 1| ≤ 3 and |x – 1| < 3 1. Evaluate |x – 1| ≤ 3 for x = {–5, –4, –3, –2, –1, 0, 1, 2, 3, 4, 5}. Determine which integers satisfy the inequality. Graph the solution set on the number line. 2. Now determine which real numbers satisfy the inequality |x – 1| ≤ 3 and graph the solution on the number line. 3. Write a compound inequality representing the second graph. Does it represent an inequality that uses the word OR or the word AND? 4. Now graph |x – 1| < 3 on a number line and write a corresponding compound inequality. What changes between the graph in step 2 and the compound inequality in step 3? 5. Using the word “distance,” explain the meaning of the graph in step 2. Then explain the meaning of the graph in step 4. 6. If you had a simple absolute value equation |x – 1| = 3, you would write two equations: x – 1 = 3 (positive equation), resulting in x = 4 x – 1 = –3 (negative equation), resulting in x = –2 Try to write two equations for |x – 1| < 3. Compare your solutions to your compound inequality from step 4? Do you notice anything? Name: ___________________________________ Algebra II Investigating Compound Inequalities Group 4 |x – 1| ≥ 3 and |x – 1| > 3 1. Evaluate |x – 1| ≥ 3 for x = {–5, –4, –3, –2, –1, 0, 1, 2, 3, 4, 5}. Determine which integers satisfy the inequality. Graph the solution set on the number line. 2. Now determine which real numbers satisfy the inequality |x – 1| ≥ 3 and graph the solution on the number line. 3. Write a compound inequality representing the second graph. Does it represent an inequality that uses the word OR or the word AND? 4. Now graph |x – 1| > 3 on a number line and write a corresponding compound inequality. What changes between the graph in step 2 and the compound inequality in step 3? 5. Using the word “distance,” explain the meaning of the graph in step 2. Then explain the meaning of the graph in step 4. 6. If you had a simple absolute value equation |x – 1| = 3, you would write two equations: x – 1 = 3 (positive equation), resulting in x = 4 x – 1 = –3 (negative equation), resulting in x = –2 Try to write two equations for |x – 1| > 3. Compare your solutions to your compound inequality from step 4? Do you notice anything?