Solve Absolute Value Inequalities

• no solution
• -6 ≤ r ≥ 8
• 6 > r > -8
• -6 < r < 8

• all real numbers
• no solution
• 0 < v < 6⁄7
• 0 ≤ v ≤ 6/7

• no solution
• all real numbers 
• -2 ≤ n ≤ 16
• n ≤ -2 or n ≥ 16

Solve.
|4m + 9| ≥ 21

• -7.5 ≤ m ≤ 3

• m ≤ -7.5 or m ≥ 3

• -3 ≤ m ≤ 7.5

• m ≤ -3 or m ≥ 7.5

Solve.

|x + 4| < 5

• x < -9 or x > 1

• -9 < x < 1

• x < 9 or x > -1

• -1 < x < 9

Solve.
|2t + ⅔| < 4

• -5/3 < t < 7/3

• t > 7/3 or t < -5/3

• -7/3 < t < 5/3

• t > 5/3 or t < -7/3

Solve.

3|d - 4| ≥ 12

• d = -8 or d = 0

• no solution

• d ≥ 8 or d ≤ 0

• d = 40 or d = 32

|4v + 12| ≥ 6

• v ≤ -4.5 or v ≥ -1.5

• -4.5 ≤ v ≤ -1.4

• -1.5 ≤ v ≤ 4.5

• v ≤ -1.5 or v ≥ 4.5

Solve.

3|2d + 9| + 13 > 10

• d > 5 or d < -1

• d < -4 or d > 5

• No Solution

• All real numbers

Solve.

|-3f| ≥ 6.3

• -18.9 ≤ f ≤ 18.9

• no solution

• f ≤ -2.1 or f ≥ 2.1

• -2.1 ≤ f ≤ 2.1