Absolute Value Inequalities

Solve.
|c + 4| < 5

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

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.3

Solve.
|y - 4| ≥ 8

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

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.3

CCSS.HSA.REI.B.3

Solve.
|y - 1| ≤ 6

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

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.3

CCSS.HSA.REI.B.3

Solve.
|p + 3| ≥ 10

• -13 ≤ p ≤ 7
• p ≤ -13 or p ≥ 7
• -7 ≤ p ≤ 13
• p ≤ -7 or p ≥ 13

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.3

CCSS.HSA.REI.B.3

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

Tags

CCSS.HSA.REI.B.3

Solve:
|x + 4| - 8 > 2

• x > 6 and x < 10
• x > 6 or x < -14
• all real numbers
• no solution

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.3

Solve:
|x + 4| + 8 > 2

• x < -3 and x > -5/3
• x < -3 and x > -4
• all real numbers
• no solution

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.3

Solve.
-5|x - 4| > 20

• x < 8 and x > 0
• x > 8 or x < 0
• all real numbers
• no solution

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.3

• - 7 < y < 3
• - 8 < y < 4
• - 7 < y < - 3
• - 8 < y < - 4

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.3

• - 1/2 ≤ z ≤ 5/2
• 1/2 ≤ z ≤ 5/2
• z ≥ 1/2 or z ≤ 5/2
• z ≤ 1/2 or z ≥ 5/2

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.3