Absolute Values Inequalities

|x| ≥ 10

• x ≥ 10 or x ≤ -10

• x ≥ -10 or x ≤ 10

• -10 ≤ x ≤ 10

• 10 ≤ x ≤ -10

| x + 3 | ≤ 2

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

| x + 1 | ≥ 3

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

| 3x - 9 | < 3

• x < - 10 or x > - 2
• -10 < x < - 2
• x < 2 or x > 4
• 2 < x < 4

Solve.
6 - 2|m -3| > -4

• -8 < m < 2
• m < -8 or m > 2
• m < -2 or m > 8
• -2 < m < 8

Solve:
3 | 2x + 7| - 7 < -4

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

• n > 1 or n < -7
• n > -1 or n < -7
• -7 < n < -1
• no solution

Solve:
|x + 4| - 8 > 2

• x > 6 and x < 10
• x > 6 or x < -14
• all real numbers
• no solution

Solve.
6 - 2|m -3| > -4

• -8 < m < 2
• m < -8 or m > 2
• m < -2 or m > 8
• -2 < m < 8

• r > 11/4 or r < 9/4
• r > 5 or r ≤ 0
• r > 5 or r < 0
• r < -5 or r > 0