Download Investigating Compound Inequalities Packet

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?