Absolute Value Inequalities

Solve:

3 | 2x + 7| - 7 < -4

• x < -3 and x > -5/3

• x < -3 and x > -4

Solve:

|x + 4| - 8 > 2

• x > 6 and x < 10

• x > 6 or x < -14

Solve.

|2x - 1| = 7

• x = -3 or x = 4

• x = 4

• x = 4 or x = -4

Solve.

-5|x - 4| > -20

• x < 8 and x > 0

• x > 8 or x < 0

• v>5 or v<-5

• v≥5 or v≤-5

• v>-5 or v<5

• x > 11 or x < 5
• x > - 11 or x > 5
• 5 < x < 11
• - 5 < x < 11

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.3

CCSS.HSA.REI.B.3

• - 4 ≤ x ≤ 6
• x ≥ - 4 or x ≤ 6
• x ≥ 4 or x ≤ - 6
• - 4 ≤ x ≤ - 6

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.3

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.
|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.

3|d - 4| = 12

• d = -8 or d = 0

• d=8 or d=0