Graphing Absolute Value Inequalities on Number Line

• v>5 or v<-5
• v≥5 or v≤-5
• v>-5 or v<5
• all real numbers

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

• 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| - 8 > 2

• x > 6 and x < 10

• x > 6 or x < -14

• all real numbers

• no solution

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.

|-3f| ≥ 6.3

• -18.9 ≤ f ≤ 18.9

• no solution

• f ≤ -2.1 or f ≥ 2.1

• -2.1 ≤ f ≤ 2.1

Solve.
|y - 1| ≤ 6

• -7 ≤ y ≤ 5

• y ≤ -7 or y ≥ 5

• -5 ≤ y ≤ 7

• y ≤ -5 or y ≥ 7