Absolute Values Inequalities

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

|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

Describe the first step in solving the absolute value inequality

• Add 5 on both sides

• Divide both sides by -5

• Set up two inequalities

• no solution

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

| 3x - 9 | < 3

• x < - 10 or x > - 2

• -10 < x < - 2

• x < 2 or x > 4

• 2 < x < 4