Inequalities and Absolute Value

Solve:
 |x + 3| > 8

• x > 5 or x < -11

• x > 5

• all real numbers

• no solution

• no solution
• a> -1/6 or a< -5/6
• a>1/2 or a< -3/2
• all real numbers

• 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.

|x + 4| < 5

• x < -9 or x > 1

• -9 < x < 1

• x < 9 or x > -1

• -1 < x < 9

Solve.

3|d - 4| ≥ 12

• d = -8 or d = 0

• no solution

• d ≥ 8 or d ≤ 0

• d = 40 or d = 32

Solve.

|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.
|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.

|d + ⅔| + ¾ < 0

• no solution

• d > -9 and d < ½

• d > -¾ and d < 9

• d < -1/12 and d > -7/12