Absolute Value Inequalities

Solve.
|c + 4| < 5

• x < -9 or x > 1
• -9 < x < 1
• x < 9 or x > -1
• -1 < x < 9

Solve.
|y - 4| ≥ 8

• y ≤ -4 or y ≥ 12
• -4 ≤ y ≤ -12
• y ≤ 4 or y ≥ -12
• -12 ≤ x ≤ 4

Solve.
|y - 1| ≤ 6

• -7 ≤ y ≤ 5
• y ≤ -7 or y ≥ 5
• -5 ≤ y ≤ 7
• y ≤ -5 or y ≥ 7

Solve.
|3c - 4| < 12

• -2 2/3 < c < 5 1/3
• c < -5 1/3  or c > 2 2/3
• c < 5 1/3 or c > -2 2/3
• -5 1/3 < c < 2 2/3

Solve.
|4k + 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

• no solution
• -6 < x < 26
• x < -6 or x > 26
• all real numbers

• No solution
• All real numbers
• -1 < a < 9/7
• -5/7 < a < 1

Solve:
 |x + 3| > 8

• x > 5 or x < -11
• x > 5
• all real numbers
• no solution

Solve:
|x + 3| > - 8

• x > 5 or x < -11
• x > 5
• all real numbers
• no solution

Solve. 
|2x - 12| + 8  = 8 

• x = 6 or x = -2
• x = 6 or x = -6
• no solution
• x = 6

Tags

CCSS.6.NS.C.7C