Introduction to Graphing Absolute Value Inequalities

Solve:
 |x + 3| > 8

• x > 5 or x < -11
• x > 5
• all real numbers
• no solution

| x + 3 | ≤ 2

• No Solution
• All Real Numbers
• -5 ≤ x ≤ -1
• 1 ≤ x ≤ 5

| x | ≤ 3.5

• No Solution
• All Real Numbers
• -3.5 ≤ x ≤ 3.5
• x ≤ -3.5  or  x ≥ 3.5

| 3c - 5 | < -2

• No Solution
• All Real Numbers
• 1 < c < ⁷/₃
• c < 1  or  c > ⁷/₃

3 | 2t - 3 | - 5 > 16

• No Solution
• All Real Numbers
• t < -2  or  t > 5
• -2 < t < 5

Solve:
|x + 4| + 8 > 2

• x < -3 and x > -5/3
• x < -3 and x > -4
• all real numbers
• no solution

Solve.
-5|x - 4| > -20

• x < 8 and x > 0
• x > 8 or x < 0
• all real numbers
• no solution

Solve the absolute Value inequality and graph. 

• A
• B
• C
• D

| x - 6 | < 4
Is this an "and"  or an "or" problem?

• and
• or

| x - 2 | > 3
Is this an "and"  or an "or" problem?

• and
• or