Solving Absolute Value Equations and Inequalities

|2a - 10| = 6

• a = 8, a = 5
• a = 2
• a = 8
• a = 8, a = 2

Evaluate each expression.
| x + 9 | = -5

• -14
• -4
• {-14, -4}
• no solution

Solve:

|x + 3| > 8

• x< -11 or x > 5

• x > 5

• all real numbers

• no solution

| 2w - 1 | < 11

• No Solution
• All Real Numbers
• -5 < w < 6
• -6 < w < 5

| x + 3 | ≤ 2

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

| k - 3 | < -1

• No Solution
• All Real Numbers
• 2 < k < 4
• k < 2  or  k > 4

| x + 1 | ≥ 3

• No Solution
• All Real Numbers
• x ≤ -4  or  x ≥ 2
• -4 ≤ x ≤ 2